A meshless numerical investigation based on the RBF-QR approach for elasticity problems

In the current research work, we present an improvement of meshless boundary element method (MBEM) based on the shape functions of radial basis functions-QR (RBF-QR) for solving the two-dimensional elasticity problems. The MBEM has benefits of the boundary integral equations (BIEs) to reduce the dimension of problem and the meshless attributes of moving least squares (MLS) approximations. Since the MLS shape functions dont have the delta function property, applying boundary conditions is not simple. Here, we propose the MBEM using RBF-QR to increase the accuracy and efficiency of MBEM. To show the performance of the new technique, the two-dimensional elasticity problems have been selected. We solve the mentioned model on several irregular domains and report simulation results

Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems. The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems. Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions