Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues

In this paper a novel Radial Basis Collocation Method (RBCM) has been applied to investigate the heterogeneous conduction and bioheat transfer problem. RBCM is a strong form meshless method which uses Radial Basis Function (RBF) interpolation to obtain the solution of the partial differential equation governing the problem under consideration. RBFs hold many advantages like exponential convergence, less dependence on the dimensionality of the problem, ability to deal with complex geometries and ease of implementation, which can be harnessed to one's benefit. Application of RBF interpolation under the framework of RBCM retains its inherent advantages provided that the errors are controlled appropriately. In this research, RBFs have been utilized to solve the steady state heterogeneous conduction and bioheat transfer problem. Approximation function is developed using inverse multiquadratic (IMQ) radial basis functions (RBFs). RBFs are infinitely differentiable functions and have global support. For heterogeneous problem, application of RBF can however become troublesome because of the nonlocality of the RBFs and errors in the domain, interface and boundary can grow large to make the problem unstable. To obtain the exponential convergence, errors at the boundaries, domain and interfaces need to be controlled. Weighted collocation has been used to overcome this problem and retain the inherent properties of the RBFs. RBCM has been successfully applied to solve strong heterogeneous heat conduction and bioheat transfer problem which shows its validity and effectiveness.

► A novel meshless method was used to obtain solution for heterogeneous conduction.
► Solution in each domain was obtained by points only in the respective domain.
► Bioheat transfer problem was solved utilizing the proposed meshless method.
► Accurate solutions were obtained for heterogeneous conduction and bioheat transfer.