Numerical solutions of partial differential equations on unbounded domain - artificial boundaries and artificial boundary conditions

Prof. Houde Han

Tsinghua University, Beijing, Popular Republic of China

In this talk we consider the numerical solutions of partial differential equations on unbounded domain. One difficulty in these problems is the unboundedness of the domain. In engineering, the usual method is to introduce an artificial boundary and to impose Dirichlet or Neumann boundary condition on it, then the problem can be reduced to a boundary value problem on a bounded computational domain. In general, the above artificial boundary conditions are very rough. In this talk, we will show how to design the artificial boundary condition with high accuracy on the given artificial boundary for various boundary value problems of partial differential equations. Then the original problem can be reduced to a boundary value problem on a bounded computational domain with high accuracy. problem.