A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems
This work addresses the computational bottleneck of dense matrices in BEM for engineering simulations, offering a faster method with exact geometry representation.
The paper presents a fast isogeometric boundary element method (BEM) for 3D Laplace and Helmholtz problems, achieving high convergence rates by combining NURBS geometry with an interpolation-based fast multipole method. Numerical examples demonstrate extremely high rates of convergence for pointwise potential.
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.