Poisson-Boltzmann Equation Solver Research Articles

Parallel adaptive mesh-refining scheme on a three-dimensional unstructured tetrahedral mesh and its applications

The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N 1.5 for N proc ⩽ 32 . Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson–Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.

Geometry-guided computation of 3D electrostatics for large biomolecules

Electrostatic interactions play a central role in biological processes. Development of fast computational methods to solve the underlying Poisson–Boltzmann equation (PBE) is vital for biomolecular modeling and simulation package. In this paper, we propose new methods for efficiently computing the electrostatic potentials for large molecules by using the geometry of the molecular shapes to guide the computation. The accuracy and stability of the solution to the PBE is quite sensitive to the boundary layer between the solvent and the solute which defines the molecular surface. In this paper, we present a new interface-layer-focused PBE solver. First, we analytically construct the molecular surface of the molecule and compute a distance field from the surface. We then construct nested iso-surface layers outwards and inwards from the surface using the distance field. We have developed a volume simplification algorithm to adaptively adjust the density of the irregular grid based on the importance to the PBE solution. We have generalized the finite difference methods using Taylor series expansion on the irregular grids. Our algorithm achieves about three times speedup in the iterative solution process of PBE, with more accurate results on an analytical solvable testing case, compared with the popular optimized DelPhi program.