arXiv subjects

E. O. Asante-Asamani

Publications and source records attributed to E. O. Asante-Asamani.

3 recordsLinked to original sources

arXiv2024

A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems

A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Padé (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20 times speed in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.

math.NA↗

arXiv2020

A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting

A second-order $L$-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.

math.NA↗

arXiv2016

A Cylindrical Basis Function for Solving Partial Differential Equations on Manifolds

Numerical solutions of partial differential equations (PDEs) on manifolds continues to generate a lot of interest among scientists in the natural and applied sciences. On the other hand, recent developments of 3D scanning and computer vision technologies have produced a large number of 3D surface models represented as point clouds. Herein, we develop a simple and efficient method for solving PDEs on closed surfaces represented as point clouds. By projecting the radial vector of standard radial basis function(RBF) kernels onto the local tangent plane, we are able to produce a representation of functions that permits the replacement of surface differential operators with their Cartesian equivalent. We demonstrate, numerically, the efficiency of the method in discretizing the Laplace Beltrami operator.

math.NA↗