A fast algorithm for particle simulations
Journal of Computational Physics
Numerical approximation of a free boundary problem arising in electromagnetic shaping
SIAM Journal on Numerical Analysis
Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates
SIAM Journal on Numerical Analysis
Hi-index | 0.00 |
In the present paper we combine an energy variational approach with shape optimization techniques to compute numerically free surfaces in electromagnetic shaping and levitation of liquid metals in three dimensions. Assuming the domains to be starshaped, the surfaces are represented via an ansatz by spherical harmonics, which generalizes the approximation by Fourier series in two dimensions. We will show that all ingredients of the shape optimization algorithm, particularly the shape gradient and the cost functional, can be computed by boundary integrals. A wavelet based fast boundary element method of optimal complexity is employed for the computation of the exterior magnetic field and its Neumann-to-Dirichlet map.