Hartmann R, Pflaum C (2017)
Publication Language: English
Publication Type: Journal article, Report
Publication year: 2017
Publisher: Springer New York LLC
Pages Range: 1-28
URI: https://link.springer.com/article/10.1007/s11075-017-0407-9
DOI: 10.1007/s11075-017-0407-9
We present a Ritz-Galerkin discretization on sparse grids using prewavelets, which allows us to solve elliptic differential equations with variable coefficients for dimensions d ≥ 2. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin discretization and semi-orthogonality. This algorithm is based on standard 1-dimensional restrictions and prolongations, a simple prewavelet stencil, and the classical operator-dependent stencil for multilinear finite elements. Numerical simulation results are presented for a three-dimensional problem on a curvilinear bounded domain and for a six-dimensional problem with variable coefficients. Simulation results show a convergence of the discretization according to the approximation properties of the finite element space. The condition number of the stiffness matrix can be bounded below 10 using a standard diagonal preconditioner.
APA:
Hartmann, R., & Pflaum, C. (2017). A prewavelet-based algorithm for the solution of second-order elliptic differential equations with variable coefficients on sparse grids. Numerical Algorithms, 1-28. https://dx.doi.org/10.1007/s11075-017-0407-9
MLA:
Hartmann, Rainer, and Christoph Pflaum. "A prewavelet-based algorithm for the solution of second-order elliptic differential equations with variable coefficients on sparse grids." Numerical Algorithms (2017): 1-28.
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