Variable order panel clustering
Computing
A sparse H -matrix arithmetic: general complexity estimates
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Fast evaluation of boundary integral operators arising from an eddy current problem
Journal of Computational Physics
Proceedings of the 46th Annual Design Automation Conference
H-Matrix techniques for stray-field computations in computational micromagnetics
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
A fast elasto-plastic formulation with hierarchical matrices and the boundary element method
Computational Mechanics
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Typical panel clustering methods for the fast evaluation of integral operators are based on the Taylor expansion of the kernel function and therefore usually require the user to implement the evaluation of the derivatives of this function up to an arbitrary degree.We propose an alternative approach that replaces the Taylor expansion by simple polynomial interpolation. By applying the interpolation idea to the approximating polynomials on different levels of the cluster tree, the matrix vector multiplication can be performed in only O(npd) operations for a polynomial order of p and an n-dimensional trial space.The main advantage of our method, compared to other methods, is its simplicity: Only pointwise evaluations of the kernel and of simple polynomials have to be implemented.