A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology (Advances in Applied Mathematics and Mechanics, 2018)
In this work, element free Galerkin (EFG) method is posed for solving nonlinear,reaction-diffusion systems which are often employed in mathematical modelingin developmental biology. A predictor-corrector scheme is applied, to avoid directlysolving coupled nonlinear systems. The EFG method employs the moving leastsquares (MLS) approximation to construct shape functions. This method uses only aset of nodal points and a geometrical description of the body to discretize the governingequation. No mesh in the classical sense is needed. However, a backgroundmesh is used for integration purpose. Numerical solutions for two cases of interest, theSchnakenberg model and the Gierer-Meinhardt model, in various regions are presentedto demonstrate the effects of various domain geometries on the resulting biologicalpatterns.