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We present spatial approximation for shallow water equations on a mesh of multiple rectangular blocks with different resolution in Cartesian geometry. The approximation is based on finite-difference operators that fulfill Summation By Parts (SBP) property – a discrete analogue of integration by parts. The solution continuity conditions between mesh blocks are imposed in a weak form using Simultaneous Approximation Terms (SAT) method.We show that the resulting discrete divergence and gradient operators are anti-conjugate. The important consequences are the discrete analogues for mass and energy conservation laws along with the proof of stability for linearized equations. The numerical shallow water equations model based on the presented spatial approximation is tested using problems with meteorological context. Test results prove high-order accuracy of SBP-SAT discretization. The interfaces between mesh blocks of different resolution produce no significant noise. The local mesh refinement is shown to have positive effect on the solution both locally inside the refined region and globally in the dynamically coupled areas. [ABSTRACT FROM AUTHOR]

In this paper, a versatile compound strip method (CSM) with non-uniform spline functions is developed for buckling analysis of stiffened structures. The proposed method further extends the existing CSM by permitting the flexible modification of local knots to place the stiffeners along the strip arbitrarily. In addition, a reasonable knot arrangement can achieve an accurate solving procedure with improved convergence. The displacements of stiffeners are expressed compatibly by the fundamental parameters of skin according to the beam-plate model. Consequently, the reinforcement of stiffeners is naturally incorporated by adding the beam stiffness matrix to the corresponding strips. Based on the first-order shear deformation plate theory and non-uniform spline functions, the semi-analytical formulations of stiffened structures are established. The present method provides the possibility to achieve the local mesh refinement in the finite strip methods. The convergence and validation study is demonstrated through the comparisons with the results of the existing literature solution and finite element method. In conclusion, a more efficient and applicable CSM is proposed to analyze the buckling behaviors of stiffened structures. [ABSTRACT FROM AUTHOR]

Ion flow is a phenomenon that exists in the normal operation of high-voltage direct current (HVDC) transmission lines. It will increase the electric field below the wire and poses a threat to the life and health of humans. Hence ion flow is considered in the HVDC transmission line laying design as a significant factor. However, the control equation of this phenomenon is a form of convective dominance, and it is easy to cause oscillation for its solution. In this study, a mesoscopic approach, the lattice Boltzmann method (LBM), is first proposed to solve the ion flow field. Firstly, the control equation of the ion flow field is rewritten in the form of the lattice Boltzmann equation. Secondly, reducing the computation load of the model by using local mesh refinement. Then a new mesh refinement method based on distribution function is proposed and compared with several other methods. Thirdly, the analytical solutions of the coaxial cylinder model are compared with LBM results, and a measuring platform is set up also for verification. Finally, the three-layer grid is successfully applied in an 800 kV unipolar full-scale transmission line. [ABSTRACT FROM AUTHOR]

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient tool to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed, and each cubic cell is treated as an SBFE subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with a particular class of transition elements on the subdomains' surfaces. Thus, a triangulation of these surfaces as executed in previous works is avoided, and consequently, the number of surface elements and degrees of freedom is reduced. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly. [ABSTRACT FROM AUTHOR]

The reliable and efficient self-adaptive analysis is a modern goal of various numerical computations. Most adaptivity methods, however, adopt energy norm to measure errors, which may not be the most natural and convenient means, e.g., for problems with locally singular gradient of displacement. Based on the Element Energy Projection (EEP) super-convergent technique in the Finite Element Method of Lines (FEMOL) which is a general and powerful semi-discrete method, reliable error estimates of displacements in maximum norm can be obtained anywhere on the FEMOL mesh and hence adaptive FEMOL by maximum norm becomes feasible. However, to tackle singularity problems effectively and efficiently, an automatic and flexible local mesh refinement strategy is required to generate meshes of high quality for more efficient adaptive FEMOL analysis. Taking the two-dimensional Poisson equation as the model problem, the paper firstly introduces the FEMOL and EEP methods with interface sides resulting from local mesh refinement. Then a local mesh refinement strategy and corresponding adaptive algorithm are presented. The numerical results given show that the proposed adaptive FEMOL with local mesh refinement can produce displacement solutions satisfying the specified tolerances in maximum norm and the adaptively-generated meshes reasonably reflect the local difficulties inherent in the physical problems without much redundant accuracy. [ABSTRACT FROM AUTHOR]

This study presents the two-phase CFD simulation of experiments carried out on COSI facility in the frame of Pressurized Thermal Shock (PTS). PTS may occur during a cold-water injection, by the Emergency Core Cooling System (ECCS) during a Loss-Of-Coolant Accident (LOCA). The simulations were carried out using the Neptune_CFD code. A sensitivity study on Direct Contact Condensation (DCC) models was performed with a comparison with experimental data. At the end of this study, it appears that the turbulence of the free surface is rather low. Consequently, a low-turbulence heat transfer model is more appropriate. Then, two sensitivity studies on global and local mesh refinement are carried out, with the creation of an optimized mesh. This optimized mesh is used with the low-turbulence model to simulate the 40 test cases with no water level and co-current steam flow. Deviations in temperature and total condensation rate are less than 5% and 25% respectively. Finally, the condensation rate between stratified and non-stratified regions is evaluated. Condensation tends to occur in non-stratified zones, with imbalance that can be very high, reaching almost 80% of total condensation. • It concerns COSI experiments with no water level in pipe and co-current steam flow. • A Global and a Local mesh refinements are used in the Neptune_CFD code. • Sensitivity studies on Direct Contact Condensation models are carried out. • The results are compared with experimental data by evaluating global criteria. • The condensation flow rate in stratified and unstratified regions is evaluated. [ABSTRACT FROM AUTHOR]

This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson equation with homogeneous Dirichlet boundary conditions and use standard linear finite elements for its discretization. The underlying domain is assumed to be polygonal but not necessarily convex. Approximations of the normal derivatives are introduced in a standard way as well as in a variational sense. On general quasi-uniform meshes, one can show that these approximate normal derivatives possess a convergence rate close to one in L² as long as the singularities due to the corners are mild enough. Using boundary concentrated meshes, we show that the order of convergence can even be doubled in terms of the mesh parameter while increasing the complexity of the discrete problems only by a small factor. As an application, we use these results for the numerical analysis of Dirichlet boundary control problems, where the control variable corresponds to the normal derivative of some adjoint variable. [ABSTRACT FROM AUTHOR]

We prove optimal convergence rates for the discretization of a general second-order linear elliptic partial differential equation with an adaptive vertex-centered finite volume scheme. While our prior work Erath & Praetorius (2016, Adaptive vertex-centered finite volume methods with convergence rates. SIAM J. Numer. Anal. 54, 2228–2255) was restricted to symmetric problems, the present analysis also covers nonsymmetric problems and hence the important case of present convection. [ABSTRACT FROM AUTHOR]

The local red-green mesh refinement of consistent, simplicial meshes in d dimensions is considered. We give a constructive solution to the green closure problem in arbitrary dimension d. Suppose that T is a simplicial mesh and that R is an arbitrary subset of its faces, which is refined with the Coxeter-Freudenthal-Kuhn (red) refinement rule. Green refinements of simplices S ∈ T are generated to restore the consistency of the mesh using a particular placing triangulation. No new vertices are created in this process. The green refinements are consistent with the red refinement on R, the unrefined mesh regions, and all other neighboring green refinements. [ABSTRACT FROM AUTHOR]

Highlights • A multi-block sigma–coordinate is developed to simulate bed evolutions for the first time. • A multi-block sigma–coordinate can easily increase depth directional resolution. • A multi-block sigma–coordinate follows bed evolution by different numbers of horizontal layers. • A multi-block sigma–coordinate has no significant impact on the time steps within the application range. Abstract This paper aims at developing a multi-block sigma-coordinate to simulate morphological evolutions. The developed multi-block sigma-coordinate can represent a steep slope topography smoothly with different numbers of horizontal layers, without producing any truncation error and artificial flux (PGFE). The multi-block sigma–coordinate can easily increase the depth-direction resolution of the sediment transport module in the sub-regions, without the aggregation of computational points in the shallow areas which may be caused by using high resolution over the entire domain. The model is beneficial for long-term simulation of morphological evaluations in lakes where the bed slope near delta region (the sedimentary area which forms where a river enters a lake/ocean) is mostly steep, and delta keeps advancing down the lake. The multi-block sigma approach at the block interface, where the number of horizontal layers varies, allocates the flux to the neighboring cells according to two essential factors, namely "the common border length" and "satisfying continuity" which lead to defining the virtual cells. A series of numerical tests have been performed. Comparison between the numerical results, the analytical solutions, and the experimental data demonstrated an appreciable accuracy, a satisfactory performance and the efficiency of this scheme. [ABSTRACT FROM AUTHOR]

The elastic and failure analysis of three-dimensional braided composites is conducted by using realistic geometry model with local mesh refinement. The realistic geometry model is reconstructed by using micro computed tomography images. The voxel meshes are utilized to overcome the difficulties of mesh discretization for realistic geometry model of three-dimensional braided composites with complex meso-geometrical configurations. In order to improve the computational efficiency, the local voxel meshes at the braid yarn boundaries are refined to capture the detailed geometries of braid yarn and reduce the number of mesh. The stress averaging technique is applied to alleviate the local artificial stress spurious introduced from voxel meshes at braid yarn boundaries. Three kinds of computation models are used to predict the tensile properties of the braided composites, which are also compared with experimental results. The effects of braid yarn twist angle and mesh sizes on the predicted tensile behavior of the braided composites are studied further. A systematic way is provided to analyze mechanical properties of three-dimensional braided composites by using realistic voxel-based model. [ABSTRACT FROM AUTHOR]

We devise a hybrid low-order method for Bingham pipe flows, where the velocity is discretized by means of one unknown per mesh face and one unknown per mesh cell which can be eliminated locally by static condensation. The main advantages are local conservativity and the possibility to use polygonal/polyhedral meshes. We exploit this feature in the context of adaptive mesh refinement to capture the yield surface by means of local mesh refinement and possible coarsening. We consider the augmented Lagrangian method to solve iteratively the variational inequalities resulting from the discrete Bingham problem, using piecewise constant fields for the auxiliary variable and the associated Lagrange multiplier. Numerical results are presented in pipes with circular and eccentric annulus cross-section for different Bingham numbers. [ABSTRACT FROM AUTHOR]

We introduce a discretization method of boundary value problems (BVP) in the case of the two dimensional diffusion equation on a rectangular mesh with refined zones. The method consists in representing the unknown distribution and its derivatives by piecewise constant distributions (PCD) on distinct meshes together with an appropriate approximate variational formulation of the exact BVP on this piecewise constant distributions space. This method, named the PCD method, has the advantage of producing the most compact possible discrete stencil. Here, we analyze and prove the convergence of the PCD method and determine upper bounds on its convergence rate.

This article deals with error estimates for the finite element approximation of Neumann boundary control problems in polyhedral domains. Special emphasis is put on singularities contained in the solution, as the computational domain has edges and corners. Thus, we use regularity results in weighted Sobolev spaces, which allow to derive sharp convergence results for locally refined meshes. The first main result is an optimal error estimate for linear finite element approximations on the boundary in the $$L^2({\it{\Gamma}})$$ -norm for both quasi-uniform and isotropically refined meshes. Later, the approximations of Neumann control problems using the postprocessing approach are investigated, that is, first a fully discrete solution with piecewise linear state and co-state, and piecewise constant controls, is computed and afterwards, an improved control by a pointwise evaluation of the discrete optimality condition is obtained. It is shown that quadratic convergence up to logarithmic factors is achieved for this control approximation if either the singularities are weak enough or the sequence of meshes is refined appropriately. [ABSTRACT FROM AUTHOR]

A numerical simulation of a turbulent round jet issuing into a laminar crossflow is performed using the method of large-eddy simulation (LES). In order to employ LES efficiently for such multi-scale problems, the code utilises a local mesh refinement (LMR) algorithm and employs a multigrid method to solve the incompressible Navier-Stokes equations. The accuracy of several LMR implementations is assessed for the Taylor-Green vortex problem. Second order accuracy of the LES-LMR code is achieved when ghost cell pressures are computed through an approximate projection method and velocities are computed using quadratic interpolation. Three different LMR strategies for a jet in crossflow are then setup in order to assess the predictive capabilities of the method. The simulations are validated against similar LES and experimental data and excellent agreement with experimental data is found for medium and fine LMR grids, while the coarse LMR grid suffers from over-prediction of the jet centreline speed. [ABSTRACT FROM AUTHOR]

Realistic 3D finite strain analysis and crack propagation with tetrahedral meshes require mesh refinement/division. In this work, we use edges to drive the division process. Mesh refinement and mesh cutting are edge-based. This approach circumvents the variable mapping procedure adopted with classical mesh adaptation algorithms. The present algorithm makes use of specific problem data (either level sets, damage variables or edge deformation) to perform the division. It is shown that global node numbers can be used to avoid the Schönhardt prisms. We therefore introduce a nodal numbering that maximizes the trapezoid quality created by each mid-edge node. As a by-product, the requirement of determination of the crack path using a crack path criterion is not required. To assess the robustness and accuracy of this algorithm, we propose 4 benchmarks. In the knee-lever example, crack slanting occurs as part of the solution. The corresponding Fortran 2003 source code is provided. [ABSTRACT FROM AUTHOR]

In this paper, we propose the use of an efficient high-order finite difference algorithm to price options under several pricing models including the Black–Scholes model, the Merton’s jump–diffusion model, the Heston’s stochastic volatility model and the nonlinear transaction costs or illiquidity models. We apply a local mesh refinement strategy at the points of singularity usually found in the payoff of most financial derivatives to improve the accuracy and restore the rate of convergence of a non-uniform high-order five-point stencil finite difference scheme. For linear models, the time-stepping is dealt with by using an exponential time integration scheme with Carathéodory–Fejér approximations to efficiently evaluate the product of a matrix exponential with a vector of option prices. Nonlinear Black–Scholes equations are solved using an efficient iterative scheme coupled with a Richardson extrapolation. Our numerical experiments clearly demonstrate the high-order accuracy of the proposed finite difference method, making the latter a method of choice for solving both linear and nonlinear partial differential equations in financial engineering problems. [ABSTRACT FROM AUTHOR]

A multiply nested technique shallow water model is described. A new algorithm for the implementation of a two-way nesting approach is presented. The two-way nesting technique is successfully applied for 2D shallow water equations using explicit finite difference scheme. This model consists of a higher-resolution (fine grid) model with nested 3:1 embedded in a lowresolution (coarse grid) model on which covers the entire domain. The formulation of the mesh nesting algorithm of the structure grid model allows flexibility in deciding the number of meshes and the ratio of grid resolution between adjacent meshes. The two-way nesting is satisfied with an interpolating of the coarse grid domain to provide boundary conditions for the fine grid region and by updating the variables on the fine grid is suitably averaged on to the coarse grid in order to drive the coarse grid model. Several of the numerical examples are investigated to check the ability and efficiency of nested grid model. The results show indicate good performance of the nesting grid. [ABSTRACT FROM AUTHOR]

An initial-boundary value problem for a time-fractional diffusion equation is discretized in space, using continuous piecewise-linear finite elements on a domain with a re-entrant corner. Known error bounds for the case of a convex domain break down, because the associated Poisson equation is no longer $H^{2}$-regular. In particular, the method is no longer second-order accurate if quasi-uniform triangulations are used. We prove that a suitable local mesh refinement about the re-entrant corner restores second-order convergence. In this way, we generalize known results for the classical heat equation. [ABSTRACT FROM AUTHOR]

We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved. [ABSTRACT FROM AUTHOR]

Error estimates for the space-semidiscrete finite element approximation of solutions to initial boundary value problems for linear, second-order hyperbolic systems in bounded polygons [ABSTRACT FROM AUTHOR]

In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces. © 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd [ABSTRACT FROM AUTHOR]

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the capturing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, circumventing the need for a specific direction criterion. Observed phenomena such as multiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests. [ABSTRACT FROM AUTHOR]

This paper deals with optimal control problems constrained by linear elliptic partial differential equations. The case where the right-hand side of the Neumann boundary is controlled, is studied. The variational discretization concept for these problems is applied, and discretization error estimates are derived. On polyhedral domains, one has to deal with edge and corner singularities, which reduce the convergence rate of the discrete solutions, that is, one cannot expect convergence order two for linear finite elements on quasi-uniform meshes in general. As a remedy, a local mesh refinement strategy is presented, and a priori bounds for the refinement parameters are derived such that convergence with optimal rate is guaranteed. As a by-product, finite element error estimates in the H1(Ω)-norm, L2(Ω)-norm and L2(Γ)-norm for the boundary value problem are obtained, where the latter one turned out to be the main challenge. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the context of multiple constitutive models, multiple finite element formulations and crack nucleation and propagation hypotheses, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D models which is independent of the constitutive and element specific technology. Observed phenomena such as multiple crack growth and shielding emerge naturally, without specialized algorithms for calculating the crack growth direction. The algorithm consists of a sequence of mesh subdivision, mesh smoothing and element erosion steps. Element subdivision is based on the classical edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity (such as void fraction or principal stress). To assess the robustness and accuracy of this algorithm, we use classical quasi-brittle benchmarks and ductile tests. [ABSTRACT FROM AUTHOR]

Error estimates for the space semi-discrete approximation of solutions of the Wave equation in polygons G ⊂ R 2 are presented. Based on corner asymptotics of the solution, it is shown that for continuous, simplicial Lagrangian Finite Elements of polynomial degree p ≥ 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of G , the maximal rate of convergence O ( N − p / 2 ) which is afforded by the Lagrangian Finite Element approximations on quasiuniform meshes for smooth solutions is restored. Dirichlet, Neumann and mixed boundary conditions are considered. Numerical experiments which confirm the theoretical results are presented. Generalizations to nonhomogeneous coefficients and elasticity and electromagnetics are indicated. [ABSTRACT FROM AUTHOR]

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions. [ABSTRACT FROM AUTHOR]

We propose an adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). Thus it is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solutions remain smooth. Nevertheless, due to the CFL stability condition the time step is restricted and leads to time consuming simulations. Therefore, we propose a local time stepping algorithm. This approach is validated in the case of classical ID numerical tests. Then, we present a 3D application. Indeed, according to an eulerian bi-fluid formulation at low Mach, an hyperbolic system of conservation laws allows an easily parallelization and mesh refinement by "blocks". [ABSTRACT FROM AUTHOR]

In this work, a homogenized XFEM approach has been proposed to evaluate the fatigue life of an edge crack plate in the presence of discontinuities (holes, inclusions and minor cracks). In this approach, the central 20% region of the plate is discretized by fine-mesh whereas remaining 80% region is discretized by coarse mesh. In case of holes and inclusion, the 80% continuum region of the plate has been modeled with homogeneous material properties. Special transition elements are developed to maintain the displacement continuity at the junction nodes. Several problems containing discontinuities in 20% region are solved by the proposed approach. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing is a commonly adopted and effective well stimulation technique in the oil and gas extraction area. Under a mixed I/III loading condition, the crack front segmentation (i.e., the parent crack segments into echelon-shaped daughter cracks) usually occurs, which highly complicates the paths of fluid-driven cracks. This paper presents an efficient numerical model for 3D hydraulic fracturing simulation considering crack front segmentation on basis of the extended finite element method (XFEM). Solutions of the momentum balance equation and the fluid flow equation are simultaneously determined by the Newton-Raphson method along with a reduction technique. In the XFEM framework, a robust local mesh-refinement scheme of the tip-enriched elements is designed to enhance the resolution of the near-front stress field which is crucial for the determination of crack segmentation and propagation behaviors. The locally refined tip-enriched elements are then divided into a series of tetrahedra to perform high-accuracy numerical integration. After verification of the proposed approach, the effects of several critical parameters in hydraulic fracturing treatments are investigated. Results show that crack front segmentation has significant effects on the resulting crack paths and crack aperture distribution. The propagation of hydraulic fractures will be depressed on account of the stress shadow induced by overlapped segments, leading to higher pumping pressure compared to the case without considering front segmentation. The sensitivity analyses indicate that larger elastic modulus of rock formation, larger fluid viscosity, higher fluid pumping rate, and smaller fluid leak-off coefficient can alleviate the influence of crack front segmentation on the pumping pressure. Larger elastic modulus, larger fluid viscosity, higher fluid pumping rate, and greater fluid leak-off coefficient lead to smaller twisting angles of the segments and smaller overlapping ratios. • A numerical model for 3D hydraulic fracturing simulation regarding crack front segmentation is presented. • A local mesh refinement scheme fully integrated with the XFEM is introduced. • Higher pumping pressures are required to propagate the crack when considering crack front segmentation. • Sensitivity analysis is performed to investigate the effects of parameters in fracturing treatments. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a novel local mesh refinement algorithm based on transformation optics (TO) has been developed for solving the Maxwellʼs equations of electrodynamics. The new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells. The transformed anisotropic Maxwellʼs equations can be stably solved by an anisotropic FDTD method, while other subgridding or adaptive mesh refinement FDTD methods require time–space field interpolations and often suffer from the late-time instability problem. To avoid small time steps introduced by the transformation optics approach, an additional application of the mapping of the material matrix to a dispersive material model is employed. Numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based FDTD method. [Copyright &y& Elsevier]