Numerical treatment of retarded boundary integral equations by sparse panel clustering. (English) Zbl 1140.65071
The authors consider the wave equation as a boundary integral equation with a retarded potential. They discretize the equation making use of the convolution quadrature in time and of the Galerkin boundary element method in space variables. As this method implies densely populated matrices, and consequently at least quadratic complexity, they use the panel clustering approximation in order to reduce the complexity. According to this approximation, they carry out upper bounds for both storage requirements and computational complexity.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
65N38 | Boundary element methods for boundary value problems involving PDEs |
35L05 | Wave equation |
65Y20 | Complexity and performance of numerical algorithms |