Work

Laplace–Beltrami Equations and Numerical Conformal Mappings on Surfaces

Year: 2025

Type: article

Abstract: . The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian surfaces. The main challenge addressed here is the connection between Laplace–Beltrami equations on surfaces and the computation of the conformal modulus of a quadrilateral. We consider mappings of simply, doubly, and multiply connected domains. The numerical computation is based on an [Formula: see text]-adaptive finite element method. The key advantage of our approach is that it allows highly accurate computations of mappings on surfaces, including domains of complex boundary geometry involving strong singularities and cusps. The efficacy of the proposed method is illustrated via an extensive set of numerical experiments including error estimates.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/24m1656840

Authors: Harri Hakula, Antti Rasila

Institutions: Aalto University, Technion – Israel Institute of Technology, Guangdong Technion-Israel Institute of Technology

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, Li Ka Shing Foundation, National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province

Awards: G1293057066, 有关拟共形映射理论及其应用的研究, G4175871384, G6697778155