The Poisson-Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using boundary integral formulation requires mesh on the surface only, yielding accurate representations of solute, which usually complicated geometry. Here, we utilize adjoint-based analyses form two goal-oriented error estimates that allow us determine contribution each...

8 Thermal simulation module 22 8.1 Mathematical details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.1.1 The Poisson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.1.2 The linear heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.1.3 Adaptive spatiotemporal refinement . . . . ....

We develop an adaptive finite element method (AFEM) using piecewise linears on a sequence of triangulations obtained by adaptive √ 3 refinement. The motivation to consider √ 3 refinement stems from the fact that it is a slower topological refinement than the usual red or red-green refinement, and that it alternates the orientation of the refined triangles, such that certain features or singular...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

Method for aureole estimation refinement through comparisons between observed aureole and estimated aureole based on Monte Carlo Ray Tracing: MCRT is proposed. Through some experiments, it is found that the proposed method does work for refinement of aureole estimation. The experimental results also show the proposed method is validated through comparison with empirical aureole estimation equat...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...