A sparse H-matrix arithmetic. Part II: Application to multi-dimensional problems

The preceding Part I of this paper has introduced a class of matrices (H-ma trices) which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The matrices discussed in Part I are able to app roximate discrete integral operators in the case of one spatial dimension. In the present Part II, the construction of H-matrices is explained for FEM and BEM applications in two and three spatial dimensions. The orders of co mplexity of the various matrix operations are exactly the same as in Part I . In particular, it is shown that the applicability of H-matrices does not require a regular mesh. We discuss quasi-uniform unstructured meshes and th e case of composed surfaces as well. AMS Subject Classifications: 65F05, 65 F30, 65F50, 65N38, 68P05, 45B05, 35C20.