Efficient Numerical Solution of 2D Diffusion Equation on Multicore Computers

This chapter focuses the point interpolation called local radial basis function collocation method (LRBFCM). The main advantage of local numerical methods is that their system matrix is sparse or banded, which simplifies the solution procedure. Then it explores how the complex memory hierarchy, in particular the L3 cache, affects a parallel program execution of a numerical method by presenting the program‐a parallel LRBFCM meshless solution of the classical 2D diffusion test case, on a multicore multiprocessor computer architecture. The parallel speedup could be further improved through the optimization of the data structures in order to minimize the communication between cores, but that would require several interferences into the code and hence loss of generality. In this chapter, five‐noded support domains used and therefore the basis of five Hardy's multiquadrics (MQs) is used as well for the solution of the diffusion equation.