ncku-talk2014-10-23

NCTS(South)/ NCKU Math Colloquium

DATE 2014-10-23　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 吳金典教授（交大應數系）

TITLE Finite Element for Solving Shallow Water Equation on Surface via Conformal Parameterization

ABSTRACT In this talk, we present our recent works on solving shallow water equation on surface using conformal parameterization technique. Brief reviews on conformal parameterization using harmonic maps and some applications in 3-D image processing based on such global parameterization technique will be introduced. An important issue on solving the shallow water equations is to impose a non-reflective boundary (NRB) condition. Traditional approaches such as natural boundary condition, absorbing boundary or perfect matching layer (add reference), etc., can be difficult to realize if these equations are to be solved on surface. To dealt with this difficulty, we apply the conformal parameterization to transforms a PDE on surface into another PDE defined on a disk where the transformed PDE is properly scaled according to the conformal factor. Due to the simple geometry of the parametric domain, the NRB condition can be easily treated. A space time finite element method is employed to solve the transformed equation. The numerical results presented here demonstrate the effectiveness of our numerical NRB boundary treatment.

NCTS(South)/ NCKU Math Colloquium

DATE	2014-10-23　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	吳金典教授（交大應數系）

TITLE	Finite Element for Solving Shallow Water Equation on Surface via Conformal Parameterization

ABSTRACT	In this talk, we present our recent works on solving shallow water equation on surface using conformal parameterization technique. Brief reviews on conformal parameterization using harmonic maps and some applications in 3-D image processing based on such global parameterization technique will be introduced. An important issue on solving the shallow water equations is to impose a non-reflective boundary (NRB) condition. Traditional approaches such as natural boundary condition, absorbing boundary or perfect matching layer (add reference), etc., can be difficult to realize if these equations are to be solved on surface. To dealt with this difficulty, we apply the conformal parameterization to transforms a PDE on surface into another PDE defined on a disk where the transformed PDE is properly scaled according to the conformal factor. Due to the simple geometry of the parametric domain, the NRB condition can be easily treated. A space time finite element method is employed to solve the transformed equation. The numerical results presented here demonstrate the effectiveness of our numerical NRB boundary treatment.