Tensor-structured preconditioners and approximate inverse of elliptic operators in \(\mathbb R^{d}\). (English) Zbl 1185.65051
The author analyses a class of tensor-structured preconditioners for the multidimensional second-order elliptic operators in \(\mathbb{R}^d, d \geq 2\) as well as possible applications of the separable approximation for the free-space Green’s kernels in finite element-boundary element coupling methods and in the Green function formulation. Numerical experiments illustrate the efficiency of low tensor-rank approximation for Green’s kernels.
Reviewer: Constantin Popa (Constanţa)
MSC:
| 65F08 | Preconditioners for iterative methods |
| 65F50 | Computational methods for sparse matrices |
| 65F30 | Other matrix algorithms (MSC2010) |
| 46B28 | Spaces of operators; tensor products; approximation properties |
| 47A80 | Tensor products of linear operators |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
preconditioning; high dimensions; boundary value problems; spectral problems; tensor approximation; Green’s kernels; elliptic resolvent; second-order elliptic operators; numerical experimentsReferences:
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