Approximation of integral operators by Green quadrature and nested cross approximation
This work addresses the need for efficient storage and computation in boundary element methods, but the improvement is incremental over existing H²-matrix techniques.
The paper presents a fast algorithm for constructing data-sparse approximations of matrices from integral equation methods for elliptic PDEs, achieving O(n k) storage for an n×n matrix where k depends on accuracy.
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in combination with quadrature to obtain a first approximation of the kernel function and then applies nested cross approximation to obtain a more efficient representation. The resulting $\mathcal{H}^2$-matrix representation requires $\mathcal{O}(n k)$ units of storage for an $n\times n$ matrix, where $k$ depends on the prescribed accuracy.