Benchmark problems in the field of numerical methods for non-local operators
The benchmark problems have been selected in order to evaluate different methods for solving problems resp. sub-problems in the field of numerical methods for non-local operators.
The main criterium should be the performance of the programme depending on the:
a) CPU-time as a function of the discretization error.
b) Convergence behaviour as a function of the number of unknowns.
c) Storage requirements as a function of the number of unknowns.
The tests should allow
to determine the class of problems for which the program is applicable. Hence, the set of test problems should contain
- different geometries as, e.g., surface with edges/corners, smooth sufaces, curved surfaces, polyhydral surfaces
- different integral operators as, e.g., single-/douple layer potential for Laplace, Helmholtz, elasticity, Maxwell, EFIE
- systems of integral equations (e.g., in connection with mixed boundary conditions)
- operators depending on parameters (e.g., wave number for the Helmholtz equation, Lamé-numbers, parameter-dependent geometries (brick with degenerate height))
- different error measures as energy norm, negative norms, field point evaluations
to compare the efficiency of different methods for various numerical subproblems as, e.g.,
- (numerical) integration
- sparse representation of integral operators
- solvers for the linear system
