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Sparse grids for boundary integral equations. (English) Zbl 0935.65131

The paper focuses on sparse grid discretizations for boundary integral equations applied to a 2-D unit square embedded in \(\mathbb{R}^3\). Important aspects such as approximating rates, preconditioning, aspectivity and compressions are discussed theoretically and also illustrated in some numerical tests, including piecewise constant and linear functions applied the single layer potential equation.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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