By Thomas Apel, Olaf Steinbach

ISBN-10: 3642303153

ISBN-13: 9783642303159

ISBN-10: 3642303161

ISBN-13: 9783642303166

This quantity on a few fresh facets of finite aspect tools and their purposes is devoted to Ulrich Langer and Arnd Meyer at the get together in their sixtieth birthdays in 2012. Their paintings combines the numerical research of finite aspect algorithms, their effective implementation on cutting-edge architectures, and the collaboration with engineers and practitioners. during this spirit, this quantity includes contributions of former scholars and collaborators indicating the extensive diversity in their pursuits within the idea and alertness of finite point methods.

Topics disguise the research of area decomposition and multilevel equipment, together with hp finite parts, hybrid discontinuous Galerkin equipment, and the coupling of finite and boundary point tools; the effective answer of eigenvalue difficulties with regards to partial differential equations with functions in electric engineering and optics; and the answer of direct and inverse box difficulties in good mechanics.

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**Example text**

K + α + β )! )2 k! (k + β )! , k=0 k=0 n the solution is given by λ = −1 S and c = 1S D−1 b. The value of the minimum is S−1. DD Preconditioning for High Order Hybrid DG Methods 39 By means of the Paule/Schorn implementation [35] of Gosper’s algorithm, V. Pillwein computed (n + α + 1)! (n + α + β + 1)! α ! (α + 1)! n! (n + β )! S= More on computer algebra techniques in finite element methods is found in [39]. We continue with a hand-proof for the asymptotic behavior: n c(α ) ∑ (k + 1)α (k + β + 1)α +1 S k=0 n α +1 k=0 j=0 = c(α ) ∑ (k + 1)α c(α ) α +1 ∑ j=0 α +1 (k + 1) j β α +1− j j ∑ α +1 (n + 1) j+α +1β α +1− j j = c(α )(n + 1)α +1(n + β + 1)α +1.

15 GHz), 8 GB GDDR5 ECC memory and achieves 515 Gflops double precision peak performance. 2 + 4 × 515) = 10972), and a 40 GB/s QDR Infiniband is used as interconnect. 2 Performance Numbers The group of Gundolf Haase in Graz is involved in several projects related to parallel computing in application areas. In the CARP project by Gernot Plank fast solvers for potential problems (as subproblem of the bidomain equations) with anisotropic varying coefficients in the domain of a heart are needed. The discretization is based on unstructured tetrahedrons.

Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence. Appl. Math. Comp. 19, 347–358 (1986) Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes Joachim Sch¨oberl and Christoph Lehrenfeld Abstract. Hybrid discontinuous Galerkin methods are popular discretization methods in applications from fluid dynamics and many others. Often large scale linear systems arising from elliptic operators have to be solved.

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