Name
Title | ||
|---|---|---|
A second order virtual node method for elliptic problems with interfaces and irregular domains |
Abstract | ||
|---|---|---|
We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L^~. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2010.05.002 | J. Comput. Physics |
Keywords | Field | DocType |
virtual node methods,order virtual node method,special virtual node,lagrange multiplier approach,general case,embedded approach,elliptic interface problems,embedded interface methods,numerical experiment,5-point finite difference stencil,irregular domain,variational methods,numerical stencil,interface problem,elliptic problem,5-point stencil,order accuracy,dirichlet boundary condition,lagrange multiplier,second order,poisson equation,finite difference,variational method | Discretization,Boundary value problem,Mathematical optimization,Regular grid,Dirichlet problem,Mathematical analysis,Finite difference,Stencil,Discontinuity (linguistics),Dirichlet boundary condition,Mathematics | Journal |
Volume | Issue | ISSN |
229 | 18 | Journal of Computational Physics |
Citations | PageRank | References |
38 | 1.38 | 28 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jacob Bedrossian | 1 | 39 | 3.60 |
| James H. von Brecht | 2 | 93 | 6.45 |
| Siwei Zhu | 3 | 46 | 3.39 |
| Eftychios Sifakis | 4 | 1100 | 59.78 |
| Joseph Teran | 5 | 1286 | 61.85 |