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151 results on '"Wick, T."'

2. Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers

Author

Knoke, T., Kinnewig, S., Beuchler, S., Demircan, A., Morgner, U., and Wick, T.

Subjects
Mathematics - Numerical Analysis, 35Q61, 65N22, 68T07
Abstract

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions., Comment: 17 pages, 11 figures, 2 tables

Published
2023

4. Soliton compression and supercontinuum spectra in nonlinear diamond photonics

Author

Melchert, O., Kinnewig, S., Dencker, F., Perevoznik, D., Willms, S., Babushkin, I., Wurz, M., Kues, M., Beuchler, S., Wick, T., Morgner, U., and Demircan, A.

Subjects
Physics - Optics, Physics - Computational Physics
Abstract

We numerically explore synthetic crystal diamond for realizing novel light sources in ranges which are up to now difficult to achieve with other materials, such as sub-10-fs pulse durations and challenging spectral ranges. We assess the performance of on-chip diamond waveguides for controlling light generation by means of nonlinear soliton dynamics. Tailoring the cross-section of such diamond waveguides allows to design dispersion profiles with custom zero-dispersion points and anomalous dispersion ranges exceeding an octave. Various propagation dynamics, including supercontinuum generation by soliton fission, can be realized in diamond photonics. In stark contrast to usual silica-based optical fibers, where such processes occur on the scale of meters, in diamond millimeter-scale propagation distances are sufficient. Unperturbed soliton-dynamics prior to soliton fission allow to identify a pulse self-compression scenario that promises record-breaking compression factors on chip-size propagation lengths.

Published
2022

5. Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model

Author

Beuchler, S., Endtmayer, B., Lankeit, J., and Wick, T.

Subjects
Mathematics - Numerical Analysis
Abstract

In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier-Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.

Published
2022

6. Multigoal-oriented error estimation and mesh adaptivity for fluid-structure interaction

Author

Ahuja, K., Endtmayer, B., Steinbach, M. C., and Wick, T.

Subjects
Mathematics - Numerical Analysis, 65N30, 65N50, 74F10
Abstract

In this work, we consider multigoal-oriented error estimation for stationary fluid-structure interaction. The problem is formulated within a variational-monolithic setting using arbitrary Lagrangian-Eulerian coordinates. Employing the dual-weighted residual method for goal-oriented a posteriori error estimation, adjoint sensitivities are required. For multigoal-oriented error estimation, a combined functional is formulated such that several quantities of interest are controlled simultaneously. As localization technique for mesh refinement we employ a partition-of-unity. Our algorithmic developments are substantiated with several numerical tests such as an elastic lid-driven cavity with two goal functionals, an elastic bar in a chamber with two goal functionals, and the FSI-1 benchmark with three goal functionals., Comment: 26 pages, 8 figures, 9 tables

Published
2021

8. Hierarchical DWR Error Estimates for the Navier Stokes Equation: $h$ and $p$ Enrichment

Author

Endtmayer, B., Langer, U., Thiele, J. P., and Wick, T.

Subjects
Mathematics - Numerical Analysis
Abstract

In this work, we further develop multigoal-oriented a posteriori error estimation for the nonlinear, stationary, incompressible Navier-Stokes equations. It is an extension of our previous work [B. Endtmayer, U. Langer, T. Wick: Two-side a posteriori error estimates for the DWR method, $SISC$, 2019, accepted]. We now focus on $h$ mesh refinement and $p$ enrichment for the error estimator. These advancements are demonstrated with the help of a numerical example

Published
2019

10. Efficient Monolithic Solvers for Fluid-Structure Interaction Applied to Flapping Membranes

Author

Jodlbauer, D., Langer, U., Wick, T., Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Brenner, Susanne C., editor, Chung, Eric, editor, Klawonn, Axel, editor, Kwok, Felix, editor, Xu, Jinchao, editor, and Zou, Jun, editor

Published
2022
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11. Multigoal-Oriented Error Estimates for Non-linear Problems

Author

Endtmayer, B., Langer, U., and Wick, T.

Subjects
Mathematics - Numerical Analysis
Abstract

In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the Partial Differential Equation (PDE) and the goal functionals may be nonlinear. Our method is based on a posteriori error estimates in which the adjoint problem is used and a partition-of-unity is employed for the error localization that allows us to formulate the error estimator in the weak form.We provide a careful derivation of the primal and adjoint parts of the error estimator. The second objective is concerned with balancing the nonlinear iteration error with the discretization error yielding adaptive stopping rules for Newton's method. Our techniques are substantiated with several numerical examples including scalar PDEs and PDE systems, geometric singularities, and both nonlinear PDEs and nonlinear goal functionals. In these tests, up to six goal functionals are simultaneously controlled., Comment: This work has been supported by the Austrian Science Fund (FWF) under the grant P 29181 `Goal-Oriented Error Control for Phase-Field Fracture Coupled to Multiphysics Problems'. The first author thanks the Doctoral Program on Computational Mathematics at JKU Linz the Upper Austrian Goverment for the support when starting the preparation of this work

Published
2018

12. Parallel Block-Preconditioned Monolithic Solvers for Fluid-Structure-Interaction Problems

Author

Jodlbauer, D., Langer, U., and Wick, T.

Subjects
Mathematics - Numerical Analysis, 65N30, 65M60, 49M15, 35Q74
Abstract

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large, ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom, and, in addition, exhibit superlinear grow in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block $LDU$-factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two- and three-dimensional test cases permitting large deformations.

Published
2018

19. Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model

Author

Beuchler, S., Endtmayer, B., Lankeit, J., and Wick, T.

Subjects
Mechanics of Materials, FOS: Mathematics, General Materials Science, Numerical Analysis (math.NA), Mathematics - Numerical Analysis
Abstract

In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier-Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.

Published
2023

25. Final Report

Author

Akhbari, D., primary, Akkutlu, Y, additional, Altman, S. J., additional, Aman, M, additional, Aminzadeh, B, additional, Arbogast, T., additional, Bagaria, H. G., additional, Balhoff, M, additional, Bauer, S. J., additional, Bennett, P. C., additional, Bhagmane, J., additional, Bielawski, C. W., additional, Bishop, J. E., additional, Biswal, S. L., additional, Bollinger, J. A., additional, Bowden, M. E., additional, Boyd, V., additional, Broome, S. T., additional, Bryant, S., additional, Bryndzia, T, additional, Butler, D, additional, Cardenas, B, additional, Cassidy, M, additional, Cha, M, additional, Chan, M.A., additional, Chang, C, additional, Chaudhary, k, additional, Chen, X., additional, Chen, H, additional, Chen, Y, additional, Chini, G. P., additional, Choens, C, additional, Chojnicki, Kirsten, additional, Chung, D H, additional, Cole, D. R., additional, Cornell, K. A., additional, Craddock, P, additional, Criscenti, L. J., additional, Cui, L, additional, Cygan, R T, additional, Daigle, H, additional, Daniel, S R, additional, Davison, S M, additional, Dehghanpour, H, additional, Delshad, M, additional, Deng, W, additional, Dewers, T A, additional, DiCarlo, D, additional, Dong, J, additional, Duan, Z, additional, Eichhubl, P, additional, Elhag, A S, additional, Ellison, C J, additional, Espinoza, D N, additional, Estep, D, additional, Evans, J, additional, Fanizza, M F, additional, Foster, L M, additional, Foster, E L, additional, Fouke, B W, additional, Ganis, B, additional, Geier, M, additional, Ghosh, R, additional, Gilbert, K, additional, Gomez, S, additional, Guiltinan, E J, additional, Hackley, P C, additional, Hardy, C D, additional, Hart, D B, additional, Hayman, N W, additional, He, B, additional, Heath, J E, additional, Hernandez-Uribe, L. Alberto, additional, Hess, N J, additional, Hesse, M A, additional, Hirasaki, G J, additional, Ho, T A, additional, Ho, J, additional, Hosseini, S A, additional, Hu, M, additional, Huang, C S, additional, Hueckel, T, additional, Huh, C, additional, Hung, C H, additional, Ilgen, A G, additional, Illangasekare, T. H., additional, Ingram, D R, additional, Iqbal, M, additional, Islan, A, additional, Jammoul, M, additional, Javier, K J, additional, Jensen, E W, additional, Jessen, K, additional, Jiang, H, additional, Jin, S, additional, Joekar-Niasar, V, additional, Johnston, K P, additional, Jung, J, additional, Jung, H, additional, Juntunen, M, additional, Kang, Q, additional, Katz, L, additional, Kelemen, P B, additional, Kelkar, C W, additional, Kelly, E D, additional, Ketcham, R A, additional, Kharaka, Y K, additional, Kianinejad, A, additional, Killough, J E, additional, Kim, S, additional, Kim, K, additional, Kim, M F, additional, Kirk, M F, additional, Kitnidis, P, additional, Kmetz, A A, additional, Kneafsey, T J, additional, Kobos, P, additional, Kong, X, additional, Kotsmar, C, additional, Krafczyk, M, additional, Krishnamurthy, P G, additional, Kruichak, J N, additional, Kucala, A, additional, Kumar, K, additional, Kwok, A, additional, Lake, L, additional, Larson, E S, additional, Larson, T E, additional, Lee, S, additional, Lee, Y J, additional, Lee, J, additional, Lee, W, additional, Leist, E A, additional, Leung, W, additional, Leung, J Y, additional, Leung, Y, additional, Liang, Y, additional, Lin, E L, additional, Lisabeth, H P, additional, Liu, R, additional, Liu, H, additional, Liu, Z C, additional, Lotfollahi, M, additional, Luo, L S, additional, Lützenkirchen, J, additional, Lyon, B A, additional, Ma, K, additional, Maisano, J A, additional, Major, J R, additional, Martinez, M J, additional, Matteo, E, additional, McFadden, C, additional, McGrath, L K, additional, McKenna, S A, additional, McNeece, C J, additional, Meckel, T A, additional, Mehmani, A, additional, Mehmani, Y, additional, Merino, E, additional, Metaxas, A E, additional, Mikelić, A, additional, Milner, T E, additional, Mirzaei, M, additional, Moaseri, E, additional, Mozley, P S, additional, Myshakin, E M, additional, Nakshatrala, K B, additional, Neilson, B M, additional, Newell, P, additional, Nguyen, Q P, additional, Noble, D R, additional, Noguera, J A, additional, Olson, J E, additional, Omelon, C R, additional, Oostrom, M, additional, Ortiz, M R, additional, Ovaysi, S, additional, Parks, M L, additional, Pasquali, A, additional, Pastora, L E, additional, Pencheva, G, additional, Pennell, K D, additional, Perego, M, additional, Perkins, W A, additional, Person, M, additional, Peterman, A H, additional, Petersen, R T, additional, Phan, S, additional, Pike, D Q, additional, Prigiobbe, V, additional, Prodanovic, M, additional, Pyrak-Nolte, L J, additional, Quintanilla, H, additional, Raduha, S, additional, Rakowski, C L, additional, Ramos, M J, additional, Reber, J E, additional, Reddy, P R, additional, Requeiro, R A, additional, Richmond, M C, additional, Rinehart, A G, additional, Roach, C M, additional, Roberts, M, additional, Romanak, K D, additional, Romanov, V N, additional, Romero-Gomez, P, additional, Ruoff, R S, additional, Sanford, R A, additional, Santamarina, J C, additional, Santillan, E F U, additional, Sathaye, K J, additional, Scheibe, T D, additional, Schonherr, M, additional, Sen, M K, additional, Senthilnathan, S, additional, Serkowski, J A, additional, Shafiei, M, additional, Shanahan, T M, additional, Shao, S, additional, Sheehan, B, additional, Sheikh, A H El, additional, Shi, Z, additional, Shovkun, I A, additional, Singh, G, additional, Singh, R, additional, Slottke, D T, additional, Sobolik, S, additional, Srinivasan, S, additional, Stadler, G, additional, Stauffer, P H, additional, Stockli, D F, additional, Stormont, J, additional, Strack, E A, additional, Strathmann, T J, additional, Suarez-Rivera, R, additional, Sun, Z, additional, Sun, Y, additional, Sun, A, additional, Sun, T, additional, Sweetser, J D, additional, Taha, M Reda, additional, Tang, H, additional, Tang, Y, additional, Tartakovsky, A M, additional, Tartakovsky, G D, additional, Tavakoli, R, additional, Tavener, S, additional, Tenney, C M, additional, Thomassen, D, additional, Tian, X, additional, Tran, V, additional, Trask, N, additional, Trevisan, L, additional, Truskett, T M, additional, Tsotsis, T T, additional, Turner, D Z, additional, Ureña-Benavides, E E, additional, Valocchi, A J, additional, Vohralik, M, additional, Wang, L, additional, Wang, W, additional, Wang, B, additional, Wang, W H, additional, Wang, Y, additional, Wen, B, additional, Werth, C J, additional, Wheeler, M, additional, White, D, additional, Wick, T, additional, Wietsma, T W, additional, Wildey, T, additional, Wilson, A, additional, Wilson, Jennifer, additional, Wolfe, W, additional, Worthen, A J, additional, Xiao, H, additional, Xue, Z, additional, Xue, G, additional, Yang, C, additional, Yang, X, additional, Yoon, H, additional, Yoon, K Y, additional, Yotov, I A, additional, Youl, A, additional, Youl, K, additional, Yu, G, additional, Zhang, L, additional, Zhang, C, additional, Zhang, R, additional, Zhen, T, additional, and Zhu, W, additional

Published
2019
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40. Mesh adaptivity for quasi‐static phase‐field fractures based on a residual‐type a posteriori error estimator.

Author

Mang, K., Walloth, M., Wick, T., and Wollner, W.

Subjects
LAGRANGE multiplier, FRACTURE mechanics, EQUATIONS
Abstract

In this work, we consider adaptive mesh refinement for a monolithic phase‐field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase‐field variational inequality realizing the fracture irreversibility constraint. The key goal is the development of a reliable and efficient residual‐type error estimator for the phase‐field fracture model in each time‐step. Based on this error estimator, error indicators for local mesh adaptivity are extracted. The proposed estimator is based on a technique known for singularly perturbed equations in combination with estimators for variational inequalities. These theoretical developments are used to formulate an adaptive mesh refinement algorithm. For the numerical solution, the fracture irreversibility is imposed using a Lagrange multiplier. The resulting saddle‐point system has three unknowns: displacements, phase‐field, and a Lagrange multiplier for the crack irreversibility. Several numerical experiments demonstrate our theoretical findings with the newly developed estimators and the corresponding refinement strategy. [ABSTRACT FROM AUTHOR]

Published
2020
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44. Parallel block‐preconditioned monolithic solvers for fluid‐structure interaction problems.

Author

Jodlbauer, D., Langer, U., and Wick, T.

Subjects
EULER'S numbers, ALGEBRAIC equations, COMPUTER simulation, ANEURYSMS, KRYLOV subspace
Abstract

Summary: In this work, we consider the solution of fluid‐structure interaction (FSI) problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian‐Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large ill‐conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom and, in addition, exhibit superlinear growth in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics‐based block preconditioners, which are derived from the block‐LDU factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two‐ and three‐dimensional test cases permitting large deformations. [ABSTRACT FROM AUTHOR]

Published
2019
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49. Virginia's Pfiesteria Monitoring Program: Water Quality

Author

Everton, Roger K., Harlan, Wick T., Priest, Jonathan W., and Alling, Mark S.

Abstract

During the summer and early fall of 1998, 34 estuarine stations in Virginia were sampled for Pfiesteria like organisms (PLOs) and associated water quality conditions. Stations were sampled either bimonthly (20 stations) or monthly (14 stations) from June to October 1998. At each station, a set of live and Lugol' s preserved samples were collected for presumptive counts of PLOs and water quality conditions were determined. Water quality parame­ters measured included standard field parameters, nutrients (total, dissolved, and particulate), chlorophyll a, and conventional water quality indicators. Although PLOs were relatively low in 1998 as compared to 1997, presump­tive PLO counts revealed higher PLO levels at stations located in the Northern Neck area (Potomac Embayments, Rappallannock River, and other smaller watersheds). The water quality parameters of pH, dissolved oxygen, and temperature were correlated with higher PLO counts, while several nutrients, salinity, and turbidity ,vere negatively correlated with PLOs. In the August 1997, relatively minor fish kills in the Pocomoke River and the Pocomoke Sound on the Virginia and Maryland border were attnbuted to the toxic dinoflagellate, Pfiesteria piscicida. Pfiesteria piscicida was first identified as a fish-killing dinoflagellate in fish tank at North Carolina State University (Noga et al., 1993 ). Pfiesteria piscicda has since been implicated in large widespread fish kills in North Carolina's estuaries (Burkholder et al., 1992, 1995).

Published
1999
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