Adaptive Cross Approximation for BEM in Elasticity

Boundary element methods (BEM) have obtained a mature state in the last years so that industrial applications are possible. However, to treat real-world problems, the so-called fast methods are necessary to reduce the original quadratic complexity to an almost linear order. Essentially, two methods are popular, the so-called fast multipole method, which uses a kernel expansion, and the algebraic approach based on ℋ-matrices with the adaptive cross approximation (ACA) to compress the matrix blocks. The latter is frequently used for scalar-valued problems, but for vector-valued problems, a modification of the pivot strategy is required. It has been suggested to search for the largest singular value out of all minimal singular values of the fundamental solution blocks. This strategy has been proposed by Rjasanow and Weggler and is studied here for elastostatics and elastodynamics. It is shown with numerical experiments that this strategy is mostly robust and results in an almost linear complexity.