H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations

Abstract : This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver.
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Submitted on : Wednesday, August 9, 2017 - 5:45:06 PM
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Luca Desiderio. H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations. Numerical Analysis [math.NA]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLY002⟩. ⟨tel-01573534⟩

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