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This report describes the research that started with the research of Floris Buwalda and continued with the work of Michaël Mersie. We will mostly work with Numerical Mathematics to find a function that expresses the power that needs to be delivered in terms of the ship’s desired speed in relation to the water. In order to keep up with the digital age where contracts and transactions are calculated to fractions of cents, it is essential that this function is as accurate as possible. We would like to take this opportunity to thank Hans Huisman and MARIN for their time and for contributing necessary data to this research., Numerical Analysis

The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). It has been shown previously that B-spline MPM can reduce grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the gridcrossing occurs more frequently, the convergence rate of B-spline MPMis lower. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate. The proposed improvement is examined in terms of the spatial convergence using the methods of manufactured solutions for large deformations., green, Numerical Analysis

In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations. Iterative solution methods are the methods of choice for these large linear systems. We start with a short introduction of Basic Iterative Methods. Thereafter preconditioned Krylov subspace methods, which are state of the art, are describeed. A distinction is made between various classes of matrices. At the end of the lecture notes many references are given to state of the art Scientific Computing methods. Here, we will discuss a number of books which are nice to use for an overview of background material. First of all the books of Golub and Van Loan [19] and Horn and Johnson [26] are classical works on all aspects of numerical linear algebra. These books also contain most of the material, which is used for direct solvers. Varga [50] is a good starting point to study the theory of basic iterative methods. Krylov subspace methods and multigrid are discussed in Saad [38] and Trottenberg, Oosterlee and Schüller [42]. Other books on Krylov subspace methods are [1, 6, 21, 34, 39]., Numerical Analysis

We carry out the global bifurcation analysis of the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. Using the Wintner–Perko termination principle of multiple limit cycles, we solve the problem on the maximum number and distribution of limit cycles in this system. Numerical experiments are done to illustrate the obtained results., Numerical Analysis

Biogrout is a method to strengthen granular soil, which is based on microbial-induced carbonate precipitation. To model the Biogrout process, a reactive transport model is used. Since high flow rates are undesirable for the Biogrout process, the model equations can be solved with a standard Galerkin finite element method. The Biogrout process involves the injection of dense fluids in the subsurface. In this paper, we present our reactive transport model for Biogrout and use it to simulate an experiment in which a pulse of a dense fluid is injected in a porous medium filled with water. In this experiment, front instabilities were observed in the form of fingers. The numerical simulations showed that the fingering phenomenon was less pronounced than in the experiment. By reducing the dispersion length and implementing a randomly distributed permeability field, the fingering phenomenon could be induced. Furthermore, the results of a case study to a Biogrout application are reported., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Numerical Analysis

Numerical Analysis, Geoscience and Engineering

Biogrout is a method to strengthen granular soil, which is based on microbial-induced carbonate precipitation. To model the Biogrout process, a reactive transport model is used. Since high flow rates are undesirable for the Biogrout process, the model equations can be solved with a standard Galerkin finite element method. The Biogrout process involves the injection of dense fluids in the subsurface. In this paper, we present our reactive transport model for Biogrout and use it to simulate an experiment in which a pulse of a dense fluid is injected in a porous medium filled with water. In this experiment, front instabilities were observed in the form of fingers. The numerical simulations showed that the fingering phenomenon was less pronounced than in the experiment. By reducing the dispersion length and implementing a randomly distributed permeability field, the fingering phenomenon could be induced. Furthermore, the results of a case study to a Biogrout application are reported., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Biogrout is a method for reinforcement of granular soil. In the Biogrout process, calcium carbonate is produced. This solid connects the grains, and therefore the strength of the soil is increased. The calcium carbonate is formed with the use of micro-organisms. Experiments and numerical simulations have been performed to demonstrate the process under various conditions. In this paper, it has been examined whether a reactive transport model can be used to describe a Biogrout experiment that was performed in a column with a length of 5 m. Four different models for the course of the reaction rate are considered. The concentration of micro-organisms and the reaction rate are fine-tuned in order to find a description of the experiment that is a best fit for the particular model. This is done by minimizing the error between the experimental and numerical results for the concentration of calcium carbonate and the by-product of the reaction., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also compare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous Galerkin (DG) Finite Element method with h-adaptivity to improve the efficiency of one-dimensional multiphase flow simulations. For smooth initial boundary value problems we show that the DG method converges with the theoretical rate and that the growth rate and phase shift of small, harmonic perturbations exhibit superconvergence. We employ two techniques to accurately and efficiently represent discontinuities. Firstly artificial diffusion in the neighbourhood of a discontinuity suppresses spurious oscillations. Secondly local mesh refinement allows for a sharper representation of the discontinuity while keeping the amount of work required to obtain a solution relatively low. The proposed DG method is shown to be superior to FV., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have low-rank off-diagonal structure, which allows the matrix-matrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear system by MSSS matrix approximations with low off-diagonal rank. In this manuscript, we analyze the convergence properties of such preconditioners. We show that the spectrum of the preconditioned system is contained in a circle centered at (1, 0) and give an analytic bound of the radius of this circle. This radius can be made arbitrarily small by properly setting a parameter in the MSSS preconditioner. Our results apply to a wide class of linear systems. The system matrix can be either symmetric or unsymmetric, definite or indefinite. We demonstrate our analysis by numerical experiments., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Networks for the high-voltage distribution of electrical energy are currently undergoing farreaching developments. National power grids are evolving fromstatic entities, producingmainly a uni-directional flow from generation to loads, to more dynamic and decentralized structures. These emerging power systems should accommodate the local generation by renewable sources and peak demands of electrical vehicle charging. The cross-border interconnection of power grids further imposes new challenges in the design, planning and daily operation of these networks. In this paper Domenico Lahaye and Kees Vuik describe recentwork by the chair of numerical analysis at the TU Delft on the numerical simulation of electrical power networks., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The Helmholtz solver is Bi-CGSTAB preconditioned with the shifted Laplace matrix-dependent multigrid method. In this paper, an efficient LSM algorithm is presented using several enhancements. First of all, a frequency decimation approach is introduced that makes use of redundant information present in the data. It leads to a speedup of LSM, whereas the impact on accuracy is kept minimal. Secondly, a new matrix storage format Very Compressed Row Storage (VCRS) is presented. It not only reduces the size of the stored matrix by a certain factor but also increases the efficiency of the matrix-vector computations. The effects of lossless and lossy compression with a proper choice of the compression parameters are positive. Thirdly, we accelerate the LSM engine by graphics cards (GPUs). A GPU is used as an accelerator, where the data is partially transferred to a GPU to execute a set of operations or as a replacement, where the complete data is stored in the GPU memory. We demonstrate that using the GPU as a replacement leads to higher speedups and allows us to solve larger problem sizes. Summarizing the effects of each improvement, the resulting speedup can be at least an order of magnitude compared to the original LSM method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Simulation of current interruption is currently performed with non-ideal switching devices for large power systems. Nevertheless, for small networks, non-ideal switching devices can be substituted by arc models. However, this substitution has a negative impact on the computation time. At the same time, these simulations are useful to design switchgear. Although these simulations are for large power systems cumbersome with traditional modelling methods, the block modelling method can handle arc models for any size of networks. The main advantage of applying the block modelling method is that the computation of the analytical Jacobian matrix is possible and cheap for any number of arc models. The computation time is smaller with this approach than with the traditional approach., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also ompare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Biogrout is a method for reinforcement of granular soil. In the Biogrout process, calcium carbonate is produced. This solid connects the grains, and therefore the strength of the soil is increased. The calcium carbonate is formed with the use of micro-organisms. Experiments and numerical simulations have been performed to demonstrate the process under various conditions. In this paper, it has been examined whether a reactive transport model can be used to describe a Biogrout experiment that was performed in a column with a length of 5 m. Four different models for the course of the reaction rate are considered. The concentration of micro-organisms and the reaction rate are fine-tuned in order to find a description of the experiment that is a best fit for the particular model. This is done by minimizing the error between the experimental and numerical results for the concentration of calcium carbonate and the by-product of the reaction., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also compare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous Galerkin (DG) Finite Element method with h-adaptivity to improve the efficiency of one-dimensional multiphase flow simulations. For smooth initial boundary value problems we show that the DG method converges with the theoretical rate and that the growth rate and phase shift of small, harmonic perturbations exhibit superconvergence. We employ two techniques to accurately and efficiently represent discontinuities. Firstly artificial diffusion in the neighbourhood of a discontinuity suppresses spurious oscillations. Secondly local mesh refinement allows for a sharper representation of the discontinuity while keeping the amount of work required to obtain a solution relatively low. The proposed DG method is shown to be superior to FV., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have low-rank off-diagonal structure, which allows the matrix-matrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear system by MSSS matrix approximations with low off-diagonal rank. In this manuscript, we analyze the convergence properties of such preconditioners. We show that the spectrum of the preconditioned system is contained in a circle centered at (1, 0) and give an analytic bound of the radius of this circle. This radius can be made arbitrarily small by properly setting a parameter in the MSSS preconditioner. Our results apply to a wide class of linear systems. The system matrix can be either symmetric or unsymmetric, definite or indefinite. We demonstrate our analysis by numerical experiments., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The Helmholtz solver is Bi-CGSTAB preconditioned with the shifted Laplace matrix-dependent multigrid method. In this paper, an efficient LSM algorithm is presented using several enhancements. First of all, a frequency decimation approach is introduced that makes use of redundant information present in the data. It leads to a speedup of LSM, whereas the impact on accuracy is kept minimal. Secondly, a new matrix storage format Very Compressed Row Storage (VCRS) is presented. It not only reduces the size of the stored matrix by a certain factor but also increases the efficiency of the matrix-vector computations. The effects of lossless and lossy compression with a proper choice of the compression parameters are positive. Thirdly, we accelerate the LSM engine by graphics cards (GPUs). A GPU is used as an accelerator, where the data is partially transferred to a GPU to execute a set of operations or as a replacement, where the complete data is stored in the GPU memory. We demonstrate that using the GPU as a replacement leads to higher speedups and allows us to solve larger problem sizes. Summarizing the effects of each improvement, the resulting speedup can be at least an order of magnitude compared to the original LSM method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Networks for the high-voltage distribution of electrical energy are currently undergoing farreaching developments. National power grids are evolving fromstatic entities, producingmainly a uni-directional flow from generation to loads, to more dynamic and decentralized structures. These emerging power systems should accommodate the local generation by renewable sources and peak demands of electrical vehicle charging. The cross-border interconnection of power grids further imposes new challenges in the design, planning and daily operation of these networks. In this paper Domenico Lahaye and Kees Vuik describe recentwork by the chair of numerical analysis at the TU Delft on the numerical simulation of electrical power networks., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Simulation of current interruption is currently performed with non-ideal switching devices for large power systems. Nevertheless, for small networks, non-ideal switching devices can be substituted by arc models. However, this substitution has a negative impact on the computation time. At the same time, these simulations are useful to design switchgear. Although these simulations are for large power systems cumbersome with traditional modelling methods, the block modelling method can handle arc models for any size of networks. The main advantage of applying the block modelling method is that the computation of the analytical Jacobian matrix is possible and cheap for any number of arc models. The computation time is smaller with this approach than with the traditional approach., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also ompare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

We propose and analyze a generic multi-class kinematic wave traffic flow model: Fastlane. The model takes into account heterogeneity among driver-vehicle units with respect to speed and space occupancy: long vehicles with large headways (e.g. trucks) take more space than short vehicles with short headways (e.g. passenger cars). Moreover, and this is what makes the model unique, this effect is larger when the traffic volume is higher. This state dependent space occupancy is reflected in dynamic passenger car equivalent values. The resulting model is shown to satisfy important requirements such as providing a unique solution and being anisotropic. Simulations are applied to compare Fastlane to other multiclass models. Furthermore, we show that the characteristic velocity depends on the truck share, which is one of the main consequences of our modeling approach., Transport & Planning, Civil Engineering and Geosciences

In this report, the recent and future contributions of experts and groups of Delft University of Technology (DUT) on the topic of smart grids (SG) are presented. This may provide guidelines on how DUT can contribute in current and future SG projects, such as the current TKI project on “Smart Grid Evolution (SGE): Developing a service platform for the Internet of Energy”. The SGE project is meant to prepare for the realization of a large-scale demonstration case in Netherlands, starting in June 2016. In this demonstration case, a smart grid with at least 100.000 connections will be constructed.1 The 3TU.Federation is involved to contribute to the development of a collaborative design and decision support environment based on state-of-the-art knowledge of smart grid concepts with appropriate tool support. The representatives of DUT are Jok Tang, Cees Witteveen and Kees Vuik. In the groups headed by Cees Witteveen and Kees Vuik, the topic of smart grids is under investigation. Some of the members of these groups are interviewed, and their input is the basis of this document. Also several experts from other groups and faculties of DUT are interviewed. The list of interviewed people is not exhaustive, but it can be interpreted as an overview of the total SG expertise that DUT possesses., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point system, while the block preconditioner makes use of the block structure of the saddle-point system. For the novel global preconditioner, it is independent of the regularization parameter, while for the block preconditioner, this property does not hold. For this MSSS matrix computation approach, model order reduction algorithms are essential to obtain a low computational complexity. We study two different model order reduction approaches, one is the new approximate balanced truncation algorithm with low-rank approximated Gramians and the other is the standard Hankel blocks approximation algorithm. We test the global preconditioner and the block preconditioner for the problem of optimal control of the Poisson equation and optimal control of the convection-diffusion equation. Numerical experiments illustrate that both preconditioners give linear computational complexity and the global preconditioner yields the fewest number of iterations and computing time. Moreover, the approximate balanced truncation algorithm consumes less floating-point operations (flops) than the Hankel blocks approximation algorithm., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Three-dimensional reverse-time migration with the constant-density acoustic wave equation requires an efficient numerical scheme for the computation of wavefields. An explicit finite-difference scheme in the time domain is a common choice. However, it requires a significant amount of disk space for the imaging condition. The frequency-domain approach simplifies the correlation of the source and receiver wavefields, but requires the solution of a large sparse linear system of equations. For the latter, we use an iterative Krylov solver based on a shifted Laplace multigrid preconditioner with matrix-dependent prolongation. The question is whether migration in the frequency domain can compete with a time-domain implementation when both are performed on a parallel architecture. Both methods are naturally parallel over shots, but the frequency-domain method is also parallel over frequencies. If we have a sufficiently large number of compute nodes, we can compute the result for each frequency in parallel and the required time is dominated by the number of iterations for the highest frequency. As a parallel architecture, we consider a commodity hardware cluster that consists of multicore central processing units (CPUs), each of them connected to two graphics processing units (GPUs). Here, GPUs are used as accelerators and not as an independent compute node. The parallel implementation of the 3D migration in frequency domain is compared to a time-domain implementation. We optimize the throughput of the latter with dynamic load balancing, asynchronous I/O, and compression of snapshots. Because the frequency-domain solver uses matrix-dependent prolongation, the coarse-grid operators require more storage than available on GPUs for problems of realistic size. Due to data transfer, there is no significant speedup using GPU-accelerators. Therefore, we consider an implementation on CPUs only. Nevertheless, with the parallelization over shots and frequencies, this approach could co, Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

80 years ago, Bruce Greenshields presented the first traffic flow model at the Annual Meeting of the Highway Research Board. Since then, many models and simulation tools have been developed. We show a model tree with four families of traffic flow models, all descending from Greenshields' model. The tree shows the historical development of traffic flow modeling and the relations between models. Based on the tree we discuss the main trends and future developments in traffic flow modeling and simulation., Transport and Planning, Civil Engineering and Geosciences

We propose and analyze a generic multi-class kinematic wave traffic flow model: Fastlane. The model takes into account heterogeneity among driver-vehicle units with respect to speed and space occupancy: long vehicles with large headways (e.g. trucks) take more space than short vehicles with short headways (e.g. passenger cars). Moreover, and this is what makes the model unique, this effect is larger when the traffic volume is higher. This state dependent space occupancy is reflected in dynamic passenger car equivalent values. The resulting model is shown to satisfy important requirements such as providing a unique solution and being anisotropic. Simulations are applied to compare Fastlane to other multi-class models. Furthermore, we show that the characteristic velocity depends on the truck share, which is one of the main consequences of our modeling approach., Transport & Planning, Civil Engineering and Geosciences

Transport & Planning, Civil Engineering and Geosciences

We propose and analyze a generic multi-class kinematic wave traffic flow model: Fastlane. The model takes into account heterogeneity among driver-vehicle units with respect to speed and space occupancy: long vehicles with large headways (e.g. trucks) take more space than short vehicles with short headways (e.g. passenger cars). Moreover, and this is what makes the model unique, this effect is larger when the traffic volume is higher. This state dependent space occupancy is reflected in dynamic passenger car equivalent values. The resulting model is shown to satisfy important requirements such as providing a unique solution and being anisotropic. Simulations are applied to compare Fastlane to other multiclass models. Furthermore, we show that the characteristic velocity depends on the truck share, which is one of the main consequences of our modeling approach., Transport & Planning, Civil Engineering and Geosciences

In this report, the recent and future contributions of experts and groups of Delft University of Technology (DUT) on the topic of smart grids (SG) are presented. This may provide guidelines on how DUT can contribute in current and future SG projects, such as the current TKI project on “Smart Grid Evolution (SGE): Developing a service platform for the Internet of Energy”. The SGE project is meant to prepare for the realization of a large-scale demonstration case in Netherlands, starting in June 2016. In this demonstration case, a smart grid with at least 100.000 connections will be constructed.1 The 3TU.Federation is involved to contribute to the development of a collaborative design and decision support environment based on state-of-the-art knowledge of smart grid concepts with appropriate tool support. The representatives of DUT are Jok Tang, Cees Witteveen and Kees Vuik. In the groups headed by Cees Witteveen and Kees Vuik, the topic of smart grids is under investigation. Some of the members of these groups are interviewed, and their input is the basis of this document. Also several experts from other groups and faculties of DUT are interviewed. The list of interviewed people is not exhaustive, but it can be interpreted as an overview of the total SG expertise that DUT possesses., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Three-dimensional reverse-time migration with the constant-density acoustic wave equation requires an efficient numerical scheme for the computation of wavefields. An explicit finite-difference scheme in the time domain is a common choice. However, it requires a significant amount of disk space for the imaging condition. The frequency-domain approach simplifies the correlation of the source and receiver wavefields, but requires the solution of a large sparse linear system of equations. For the latter, we use an iterative Krylov solver based on a shifted Laplace multigrid preconditioner with matrix-dependent prolongation. The question is whether migration in the frequency domain can compete with a time-domain implementation when both are performed on a parallel architecture. Both methods are naturally parallel over shots, but the frequency-domain method is also parallel over frequencies. If we have a sufficiently large number of compute nodes, we can compute the result for each frequency in parallel and the required time is dominated by the number of iterations for the highest frequency. As a parallel architecture, we consider a commodity hardware cluster that consists of multicore central processing units (CPUs), each of them connected to two graphics processing units (GPUs). Here, GPUs are used as accelerators and not as an independent compute node. The parallel implementation of the 3D migration in frequency domain is compared to a time-domain implementation. We optimize the throughput of the latter with dynamic load balancing, asynchronous I/O, and compression of snapshots. Because the frequency-domain solver uses matrix-dependent prolongation, the coarse-grid operators require more storage than available on GPUs for problems of realistic size. Due to data transfer, there is no significant speedup using GPU-accelerators. Therefore, we consider an implementation on CPUs only. Nevertheless, with the parallelization over shots and frequencies, this approach could co, Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point system, while the block preconditioner makes use of the block structure of the saddle-point system. For the novel global preconditioner, it is independent of the regularization parameter, while for the block preconditioner, this property does not hold. For this MSSS matrix computation approach, model order reduction algorithms are essential to obtain a low computational complexity. We study two different model order reduction approaches, one is the new approximate balanced truncation algorithm with low-rank approximated Gramians and the other is the standard Hankel blocks approximation algorithm. We test the global preconditioner and the block preconditioner for the problem of optimal control of the Poisson equation and optimal control of the convection-diffusion equation. Numerical experiments illustrate that both preconditioners give linear computational complexity and the global preconditioner yields the fewest number of iterations and computing time. Moreover, the approximate balanced truncation algorithm consumes less floating-point operations (flops) than the Hankel blocks approximation algorithm., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

80 years ago, Bruce Greenshields presented the first traffic flow model at the Annual Meeting of the Highway Research Board. Since then, many models and simulation tools have been developed. We show a model tree with four families of traffic flow models, all descending from Greenshields' model. The tree shows the historical development of traffic flow modeling and the relations between models. Based on the tree we discuss the main trends and future developments in traffic flow modeling and simulation., Transport and Planning, Civil Engineering and Geosciences

We propose and analyze a generic multi-class kinematic wave traffic flow model: Fastlane. The model takes into account heterogeneity among driver-vehicle units with respect to speed and space occupancy: long vehicles with large headways (e.g. trucks) take more space than short vehicles with short headways (e.g. passenger cars). Moreover, and this is what makes the model unique, this effect is larger when the traffic volume is higher. This state dependent space occupancy is reflected in dynamic passenger car equivalent values. The resulting model is shown to satisfy important requirements such as providing a unique solution and being anisotropic. Simulations are applied to compare Fastlane to other multi-class models. Furthermore, we show that the characteristic velocity depends on the truck share, which is one of the main consequences of our modeling approach., Transport & Planning, Civil Engineering and Geosciences

Transport & Planning, Civil Engineering and Geosciences

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU factorization of a sparse matrix from discretized PDEs in linear computational complexity with respect to the problem size. In contrast to the standard block preconditioners, we exploit the global MSSS structure of the 2 by 2 block system from the discretized Stokes equation and linearized Navier-Stokes equation. This avoids the approximation of the Schur complement, which is a big advantage over standard block preconditioners. Numerical experiments on standard CFD benchmark problems in IFISS were carried out to evaluate the performance of the MSSS preconditioners. It was illustrated that the MSSS preconditioner yields mesh size independence convergence. Moreover, the convergence is almost insensitive to the viscosity parameter. Comparison with the algebraic multigrid (AMG) method and the geometric multigrid (GMG) method, the MSSS preconditioning technique is more robust than both the AMG method and the GMG method, and considerably faster than the AMG method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this report we explore the performance of the SIMPLER , augmented Lagrangian, ’grad-div’ preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number varies from a low to the limiting number for a laminar flow., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper considers the deflated preconditioned conjugate gradient method for solving such systems. Our deflation technique uses as the deflation space the rigid body modes of sets of elements with homogeneous material properties. We show that in the deflated spectrum the small eigenvalues are mapped to zero and no longer negatively affect the convergence. We justify our approach through mathematical analysis and show with numerical experiments on both academic and realistic test problems that the convergence of our DPCG method is independent of discontinuities in the material properties., Structural Engineering, Civil Engineering and Geosciences

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that effects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity., Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU factorization of a sparse matrix from discretized PDEs in linear computational complexity with respect to the problem size. In contrast to the standard block preconditioners, we exploit the global MSSS structure of the 2 by 2 block system from the discretized Stokes equation and linearized Navier-Stokes equation. This avoids the approximation of the Schur complement, which is a big advantage over standard block preconditioners. Numerical experiments on standard CFD benchmark problems in IFISS were carried out to evaluate the performance of the MSSS preconditioners. It was illustrated that the MSSS preconditioner yields mesh size independence convergence. Moreover, the convergence is almost insensitive to the viscosity parameter. Comparison with the algebraic multigrid (AMG) method and the geometric multigrid (GMG) method, the MSSS preconditioning technique is more robust than both the AMG method and the GMG method, and considerably faster than the AMG method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this report we explore the performance of the SIMPLER , augmented Lagrangian, ’grad-div’ preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number varies from a low to the limiting number for a laminar flow., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper considers the deflated preconditioned conjugate gradient method for solving such systems. Our deflation technique uses as the deflation space the rigid body modes of sets of elements with homogeneous material properties. We show that in the deflated spectrum the small eigenvalues are mapped to zero and no longer negatively affect the convergence. We justify our approach through mathematical analysis and show with numerical experiments on both academic and realistic test problems that the convergence of our DPCG method is independent of discontinuities in the material properties., Structural Engineering, Civil Engineering and Geosciences

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that effects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity., Electrical Engineering, Mathematics and Computer Science

Biogrout is a new method for soil reinforcement, which is based on microbialinduced carbonate precipitation. Bacteria and reactants are flushed through the soil, resulting in calcium carbonate precipitation and consequent soil reinforcement. Bacteria are crucially important in the Biogrout process since they catalyse the reaction. Hence, to control the process, it is essential to know where the bacteria are located. The bacteria are possibly in suspension but can also be adsorbed or fixated on the matrix of the porous structure. In this article, a model is derived for the placement of bacteria. The model contains three phases of bacteria: bacteria in suspension, adsorbed bacteria and fixed bacteria. An analytical solution is derived for instantaneous reactions between these three phases. The analytical solution is compared to numerical simulations for finite reaction rates. For the numerical simulations the standard Galerkin Finite Element Method is used., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Electrical Engineering, Mathematics and Computer Science