Solving the Poisson equation on small aspect ratio domains using unstructured meshes

Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Solving Multidimensional Continuum Mechanics Problems on Unstructured Lagrange Meshes

The paper discusses the effort carried out at VNIIEF to consider the applicability of unstructured Lagrange meshes to multidimensional continuum mechanics problems with high shear strain and vortex flows. Three finite-difference numerical techniques for solving continuum mechanics problems on polyhedral unstructured Lagrange meshes are described. Examples of numerical calculations of benchmark ...

Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains Marcus

We present a graph-based strategy for representing the computational domain for embedded boundary discretizations of conservation-law PDE's. The representation allows recursive generation of coarse-grid geometry representations suitable for multigrid and adaptive mesh re nement calculations. Using this scheme, we implement a simple multigrid V-cycle relaxation algorithm to solve the linear elli...

Solving the Nonlinear Poisson Equation on the Unit Disk

We propose and analyze a numerical method for solving the nonlinear Poisson equation −Δu = f(·, u) on the unit disk with zero Dirichlet boundary conditions. The problem is reformulated as a nonlinear integral equation. We use a Galerkin method with polynomials as approximations. The speed of convergence is shown to be very rapid; and experimentally the maximum error is exponentially decreasing ...