2015
DOI: 10.1007/s10915-015-0109-1
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Two-Level Space–Time Domain Decomposition Methods for Three-Dimensional Unsteady Inverse Source Problems

Abstract: As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a two-level space-time domain decomposition method for solving an inverse source problem associated with the time-dependent convection-diffusion equation in three dimensions. We introduce a mixed finite element/finite difference method and a one-level and a two-level space-time parallel domain decomposition preconditioner for the Karush-Kuhn-T… Show more

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Cited by 20 publications
(10 citation statements)
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“…Here, ( f , g) Ω = ∫ Ω f · g dΩ is the standard scalar inner product in L 2 (Ω). We discretize the weak form of the LES equations (16) in space with a P 1 − P 1 stabilized finite element method. 22,23 First, we triangulate the computational domain Ω by a conformal tetrahedral mesh  h = {K} with h K the diameter of the element K ∈  h .…”
Section: Fully Implicit Finite Element Discretizationmentioning
confidence: 99%
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“…Here, ( f , g) Ω = ∫ Ω f · g dΩ is the standard scalar inner product in L 2 (Ω). We discretize the weak form of the LES equations (16) in space with a P 1 − P 1 stabilized finite element method. 22,23 First, we triangulate the computational domain Ω by a conformal tetrahedral mesh  h = {K} with h K the diameter of the element K ∈  h .…”
Section: Fully Implicit Finite Element Discretizationmentioning
confidence: 99%
“…NKS has been successfully applied to solve different kind of nonlinear problems, for example, PDE‐constrained optimization problems, fluid‐structure interaction problems, non‐Newtonian fluid problems, inverse source problems, and elasticity problems, and has shown good parallel scalability to thousands of processors. In this work, we extend the algorithm to solve the fully implicit 3D LES problems and to investigate the performance of NKS for an industrial application.…”
Section: Introductionmentioning
confidence: 99%
“…are the error vector functions of the state y and adjoint state p on each sub-interval. If we can show that both e k 1 (T 1 ) and w k 2 (T 1 ) converge to zero as k goes to infinity, then the uniqueness of the solution to both (25) and (26) obviously implies all error vector functions over each sub-interval also converge to zero as k goes to infinity.…”
Section: One-level Time Domain Decomposition Algorithms With Convergementioning
confidence: 99%
“…In (25), it follows from multiplying from the left side of the first equation with (e k 1 ) , the transpose of (e k 1 ), and the second one with (w k 1 ) , respectively,…”
Section: One-level Time Domain Decomposition Algorithms With Convergementioning
confidence: 99%
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