This report discusses an implementation [1] of an Adaptive Mesh Refinement (AMR) Poisson solver which solves Poisson’s equation using multigrid relaxation. Local refinement introduces several added issues. Special care has been taken to match the solution across coarse/fine interfaces so that the solution maintains global second order accuracy. The nested mesh hierarchy can be defined by the us...

In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers’ equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus ...

In this paper global linear independence, local linear independence and HH older continuity of the solution of the ve-coeecient reenement equation (x) = 4 X k=0 c k (3x ? k); ^ (0) = 1; are considered. Especially we construct HH older continuous solution of the above reene-ment equation which is globally linearly independent but locally linearly dependent. Also multiresolution and explicite con...

The solvability and Fredholm properties of refinement equations in spaces of square-integrable functions are studied. Necessary and jointly necessary and sufficient conditions for the solvability of homogeneous and nonhomogeneous refinement equations are established. It is shown that in the space L2(R) the kernel space of any homogeneous equation with a non-trivial solution is infinite dimensio...

In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goal-oriented indicators are not sufficient on their own to lead to a superior refinement algorithm. To remedy this, we propose a problem-specific marking strategy using the solva...