Multithreading Performance Simulating Fractional-Order Moisture Transport on Amd Epyc

Abstract

The paper studies the performance of multithreaded parallel implementation of a finite-difference solver for a two-dimensional space-fractional generalization of Richards equation. For numerical solution we used implicit Crank-Nicholson scheme with L1-approximation of Caputo fractional derivative and TFQMR linear systems’ solver. OpenMP implementation was tested on three CPUs — server Intel Xeon Bronze 3104 and AMD EPYC 7542 along with laptop AMD Ryzen 3 5300U. Testing results show that the proposed implementation can give close-to-linear acceleration when executing on up to 8 cores. On high-performance AMD EPYC maximal acceleration was achieved when 32-64 cores were used showing limited scalability of the algorithms on such a CPU.

Mathematical Modelling of Water Regulation Processes on Dual-Action Drainage Systems

“…Numerical solution of the initial-boundary value problem for the model based on Equation ( 1) is performed according to the implicit finitedifference Crank-Nicholson scheme [19] on a uniform grid with respect to the space variables with the use of the algorithm for adaptive time step selection [15].…”

“…Similarly to [15], we consider the uniform finite-difference grid , where h x , h z are the steps with respect to the spatial variables, τ is the time step. Here and further the grid analogue of the water head function h and, similarly, other functions, is designated as h h x z t ik j i k j = ( , , ).…”

“…Here and further the grid analogue of the water head function h and, similarly, other functions, is designated as h h x z t ik j i k j = ( , , ). As the results of discretization we obtain [15] the following linear system that is further solved by the TFQMR algorithm [20]:…”