Numerical Solution of the Beltrami Equation
arXiv:0802.11951 citationsh-index: 8
AI Analysis
For researchers in computational complex analysis, this provides a practical numerical method for a fundamental equation.
The paper presents an algorithm for solving the Beltrami equation in a planar disk without evaluating singular integrals, achieving efficient computation with analyzed complexity.
An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear mu-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational complexity is analyzed.