A mesh-less method to solve electrical resistance tomography forward problem using singular boundary distributed source method

Abstract

This paper presents a novel mesh-less method called singular boundary distributed source (SBDS) method to solve the electrical resistance tomography (ERT) forward problem. Mesh-less methods are mathematically simple and computationally efficient i.e. same accuracy that of mesh or domain based methods can be achieved with less computation time. The domain boundary is discretized such that the source and field points coincide on the same boundary and the solution is expressed as a linear combination of fundamental solution of governing equation. The singularity appearing due to coinciding of source and field points is addressed using a hybrid approach. The coefficients corresponding to Neumann boundary are evaluated using the improved distributed source method (IBDS) while the coefficients corresponding to Dirichlet boundary conditions are evaluated using inverse interpolation technique. The hybrid SBDS with complete electrode model is formulated for ERT forward problem. The proposed SBDS method has better accuracy and convergence as compared to other mesh-less methods. Especially, the SBDS method solution is not dependent on distributed source radius therefore is stable compared to the IBDS method. The proposed SBDS method is tested with numerical experiments and the performance is compared against boundary discretization methods such as the IBDS and boundary element methods.