A new adaptive coarse space approach including a condition number bound for FETI-DP or BDDC methods for problems with coefficient jumps inside subdomains and across subdomain boundaries in three dimensions is presente...
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Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most prom...
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The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process part...
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ISBN:
(数字)9783319519548
ISBN:
(纸本)9783319519548;9783319519531
The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process particle-based simulation data, and we highlight new aspects for the quantitative comparison with experimental data. As the underlying simulation model we consider the particle method Peridynamics, a non-local generalization of continuum mechanics. The first analysis technique is an extended component labeling algorithm to extract the fragment size and the corresponding histograms. The distribution of the fragment size can be obtained by real-world experiments as demonstrated in Schram and Meyer (Simulating the formation and evolution of behind armor debris fields. ARL-RP 109, U.S. Army Research Laboratory, 2005), Vogler et al. (Int J Impact Eng 29: 735-746, 2003). The second approach focuses on the visualization of the stress after an impact. Here, the particle-based data is re-sampled and rendered with standard volume rendering techniques to address the interference pattern of the stress wave after reflection at the boundary. For the extraction and visual analysis, we used the widely-used Stanford bunny as a complex geometry. For a quantitative study with a simple geometry, the edge-on impact experiment (Schradin, Scripts German Acad Aeronaut Res 40: 21-68, 1939;Strassburger, Int J Appl Ceram Technol 1: 1: 235-242, 2004;Kawai et al., Procedia Eng 103: 287-293, 2015) can be applied. With these new visualization approaches, new insights for the quantitative comparison of fragmentation and wave propagation become intuitively accessible.
In this work we solve efficiently 2D time dependent singularly perturbed problems. The fully discrete numerical scheme is constructed by using a two step discretization process, firstly in space, by using the classica...
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ISBN:
(数字)9783319672021
ISBN:
(纸本)9783319672021;9783319672014
In this work we solve efficiently 2D time dependent singularly perturbed problems. The fully discrete numerical scheme is constructed by using a two step discretization process, firstly in space, by using the classical upwind finite difference scheme on a special mesh of Shishkin type, and later on in time by using the fractional implicit Euler method. The method is uniformly convergent with respect to the diffusion parameter having first order in time and almost first order in space. We focus our interest on the analysis of the influence of general Dirichlet boundary conditions in the convergence of the algorithm. We propose a simple modification of the natural evaluations, which avoid the order reduction associated to those natural evaluations. Some numerical tests are shown in order to exhibit, from a practical of point of view, the robustness of the numerical method as well as the influence of the improved boundary conditions.
The direct time parallelization method based on diagonalization is only applicable to linear problems. We propose here a new method based on diagonalization which permits the direct parallelization in time of a Newton...
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Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such s...
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We consider solving linear systems with multiple shifts and multiple right-hand sides. In order to solve these linear systems efficiently, we develop the Shifted Block BiCGGR method. This method is based on the shift-...
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ISBN:
(数字)9783319624266
ISBN:
(纸本)9783319624266;9783319624242
We consider solving linear systems with multiple shifts and multiple right-hand sides. In order to solve these linear systems efficiently, we develop the Shifted Block BiCGGR method. This method is based on the shift-invariance property of Block Krylov subspaces. Using this property, the Shifted systems can be solved in the process of solving the Seed system without matrix-vector multiplications. The Shifted Block BiCGGR method can generate high accuracy approximate solutions of the Seed system. However, the accuracy of the approximate solutions of the Shifted systems may deteriorate due to the error of the matrix multiplications appearing in the algorithm. In this paper, we improve the accuracy of the approximate solutions of the Shifted systems generated by the Shifted Block BiCGGR method.
We describe preconditioned iterative methods for estimating the number of eigenvalues of a Hermitian matrix within a given interval. Such estimation is useful in a number of applications. It can also be used to develo...
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ISBN:
(数字)9783319624266
ISBN:
(纸本)9783319624266;9783319624242
We describe preconditioned iterative methods for estimating the number of eigenvalues of a Hermitian matrix within a given interval. Such estimation is useful in a number of applications. It can also be used to develop an efficient spectrum-slicing strategy to compute many eigenpairs of a Hermitian matrix. Our method is based on the Lanczos- and Arnoldi-type of iterations. We show that with a properly defined preconditioner, only a few iterations may be needed to obtain a good estimate of the number of eigenvalues within a prescribed interval. We also demonstrate that the number of iterations required by the proposed preconditioned schemes is independent of the size and condition number of the matrix. The efficiency of the methods is illustrated on several problems arising from density functional theory based electronic structure calculations.
This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the s...
ISBN:
(数字)9783319639703
ISBN:
(纸本)9783319639697
This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.
There has recently been a considerable activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants. The primal constraints of a BDDC...
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