Development and verification of a simplified HP-version of the least-squares collocation method for irregular domains

A new high-precision hp-version of the least-squares collocation method (hp-LSCM) for the numerical solution of elliptic problems in irregular domains is proposed, implemented, and verified. We use boundary irregular cells (i-cells) cut off from the cells of a rectangular grid by a boundary domain and their external parts for writing the collocation and matching equations in constructing an approximate solution. A separate solution is not constructed in small and (or) elongated non-independent i-cells. The solution is continued from neighboring independent cells, in which the outer (and inner in a multiply-connected domain) part of the domain boundary contained in these non-independent i-cells is used to write the boundary conditions. This approach significantly simplifies the computer implementation of the developed hp-LSCM in comparison with the previous well-recommended version without losing its efficiency. We show reducing the overdetermination ratio of a system of linear algebraic equations in comparison with its values in the traditional versions of LSCM when solving a biharmonic equation. The results are compared with those of other papers with a demonstration of the advantages of the new technique. We present the results of bending calculations of annular plates of various thicknesses in the framework of the Kirchhoff-Love and Reissner-Mindlin theories using hp-LSCM without shear locking.