Atomic Solution of Poisson Type Equation

Multigrid solution of the Poisson - Boltzmann equation

A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems occurring in reactor physics. A detailed a...

Cubic spline Numerov type approach for solution of Helmholtz equation

We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

Unstructured Volume - Agglomeration MG : Solution of the Poisson Equation

Efficient solution technique for solving the Poisson-Boltzmann equation

The Poisson-Boltzmann (PB) equation has been extensively used to analyze the energetics and structure of proteins and other significant biomolecules immersed in electrolyte media. A new highly efficient approach for solving PB-type equations that allows for the modeling of many-atoms structures such as encountered in cell biology, virology, and nanotechnology is presented. We accomplish these e...

The Poisson - Boltzmann Equation Analysis and Multilevel Numerical Solution

We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equatio...