Another software library on hierarchical matrices for elliptic differential equations (AHMED)
The existing theory shows that hierarchical matrix approximations with logarithmic-linear complexity can be generated at least for discretizations of non-local operators arising in the context of elliptic boundary value problems, i.e., inverses, Schur complements, and the factors of the LU decomposition of finite element stiffness matrices. Hierarchical matrices are provably robust with respect to nonsmooth coefficients appearing in the partial differential operator.
Another field of application is boundary element methods. Here, the adaptive cross approximation method can be used to construct hierarchical matrix approximations based on few of the original matrix entries.
For more information on hierarchical matrices see the monograph.
The AHMED software library is one of the most efficient implementations of the hierarchical matrix methodology. It contains functions for the following purposes:
|Hierarchical Matrix Arithmetic|
|Integral Equations in 2D and 3D|
|Finite Element Methods|
The library is written in C++. Time-critical components are based on LAPACK and BLAS. The parallel parts of the library use the MPI standard.