Solving the Laplace-Beltrami equation on S2 using spherical triangles

✍ Scribed by Jun Mu

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 559 KB
• Volume: 12
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199609)12:5<627::aid-num6>3.0.co;2-m

✦ Synopsis

The geometry of the domain -S2, causes difficulty in solving the Laplace-Beltrami Iquation, for example, in discretization for the differential equation. To overcome this problem, we study a numerical method, which is based on the finite element approximation with a hierarchical refinement of icosahedron for the grid. We construct a geometrically intrinsic base vector field for the Galerkin approximation. In this way, no artificial poles are introduced, and the numerical grids are distributed more evenly. We use radial projection to map the curved triangle onto a flat one. so that existing quadrature schemes can be applied for the numerical integration. The resulting system of linear algebraic equations is solved by using a conjugate gradient method. @