Solving PDEs With Variable Coefficients on Locally Adaptive Sparse Grids and Corresponding Refinement Strategies

Scherner-Grießhammer R, Pflaum C (2025)

Publication Type: Conference contribution

Publication year: 2025

Journal

Lecture Notes in Computational Science and Engineering Springer Verlag

Publisher: Springer Science and Business Media Deutschland GmbH

Book Volume: 154 LNCSE

Pages Range: 350-359

Conference Proceedings Title: Lecture Notes in Computational Science and Engineering

Event location: Lisbon, PRT

ISBN: 9783031861680

DOI: 10.1007/978-3-031-86169-7_36

Abstract

Using sparse grids and the L2-orthogonality of prewavelets, one can apply a Ritz-Galerkin discretization of elliptic partial differential equations (PDEs) with variable coefficients even for dimension d>3. This leads to a linear equation system with O(N(log(N)d-1)) unknowns. The theory of regular sparse grids can be extended to locally adaptive sparse grids. These are needed for several applications like PDEs with corner singularities or the high-dimensional Schrödinger equation. We introduce two different refinement strategies to obtain locally adaptive sparse grids. A numerical example shows how the correct choice of such a refinement strategy has major impact on the convergence rate of the discretization.

Authors with CRIS profile

Riccarda Scherner-Grießhammer Professur für Numerische Simulation und Hochleistungsrechnen Christoph Pflaum Professur für Numerische Simulation und Hochleistungsrechnen

How to cite

APA:

Scherner-Grießhammer, R., & Pflaum, C. (2025). Solving PDEs With Variable Coefficients on Locally Adaptive Sparse Grids and Corresponding Refinement Strategies. In Adélia Sequeira, Ana Silvestre, Svilen S. Valtchev, João Janela (Eds.), Lecture Notes in Computational Science and Engineering (pp. 350-359). Lisbon, PRT: Springer Science and Business Media Deutschland GmbH.

MLA:

Scherner-Grießhammer, Riccarda, and Christoph Pflaum. "Solving PDEs With Variable Coefficients on Locally Adaptive Sparse Grids and Corresponding Refinement Strategies." Proceedings of the European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023, Lisbon, PRT Ed. Adélia Sequeira, Ana Silvestre, Svilen S. Valtchev, João Janela, Springer Science and Business Media Deutschland GmbH, 2025. 350-359.

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