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

Griebel, M.; Oswald, P.; Schiekofer, T.

Numer. Math. 83, No. 2, 279-312 (1999).

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.

Reviewer: J.C.F.Telles (Rio de Janeiro)

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

Keywords:

boundary elements; numerical examples; boundary integral equations; preconditioning; aspectivity; single layer potential equations