The numerical solution of second-order boundary value problems on nonuniform meshes
Mathematics of Computation
Supra-convergent schemes on irregular grids
Mathematics of Computation
Elimination of adaptive grid interface errors in the discrete cell centered pressure equation
Journal of Computational Physics
Matrix-Dependent Multigrid Homogenization for Diffusion Problems
SIAM Journal on Scientific Computing
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
On the Analysis of Finite Volume Methods for Evolutionary Problems
SIAM Journal on Numerical Analysis
Mimetic discretizations for Maxwell's equations
Journal of Computational Physics
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Fast simulation of 3D electromagnetic problems using potentials
Journal of Computational Physics
Multigrid
SIAM Journal on Scientific Computing
Fast Finite Volume Simulation of 3D Electromagnetic Problems with Highly Discontinuous Coefficients
SIAM Journal on Scientific Computing
Speeding up construction of PMR quadtree-based spatial indexes
The VLDB Journal — The International Journal on Very Large Data Bases
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
Journal of Computational Physics
Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Bottom-Up Construction and 2:1 Balance Refinement of Linear Octrees in Parallel
SIAM Journal on Scientific Computing
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
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In this study we consider adaptive mesh refinement for the solution of Maxwell's equations in the quasi-static or diffusion regime. We propose a new finite volume OcTree discretization for the problem and show how to construct second order stencils on Yee grids, extending the known first order discretization stencils. We then develop an effective preconditioner to the problem. We show that our preconditioner performs well for discontinuous conductivities as well as for a wide range of frequencies.