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.
References
Richards L. A. Capillary conduction of liquids through porous mediums. Physics.1931. Vol. 1. No. 5. P. 318–333.
Pachepsky Y., Timlin D. Water transport in soils as in fractal media. Journal of Hydrology. 1988. Vol. 204. No. 1–4. P. 98–107.
Podlubny I. Fractional differential equations. New York: Academic Press, 1999.
Pachepsky Y., Timlin D., Rawls W. Generalized Richards’ equation to simulate water transport in unsaturated soils. Journal of Hydrology. 2003. Vol. 272. P. 3–13.
Kandelous M. M, Kamai T., Vrugt J. A., Simunek J., Hanson B., Hopmans J. W. Evaluation of subsurface drip irrigation design and management parameters foralfalfa. Agricultural Water Management. 2012. Vol. 109. P. 81–93.
Egidi N., Gioia E., Maponi P., Spadoni L. A numerical solution of Richards equation: a simple method adaptable in parallel computing. International Journal of Computer Mathematics. 2020. Vol. 97. No. 1–2, P. 2–17.
Romashchenko M., Bohaienko V., Matiash T., Kovalchuk V., Krucheniuk A. Numerical simulation of irrigation scheduling using fractional Richards equation. Irrigation Science. 2021. Vol. 39. No. 3. P. 385–396.
Bohaienko V. O. Parallel algorithms for modelling two-dimensional non-equilibrium salt transfer processes on the base of fractional derivative model. Fractional Calculus and Applied Analysis. 2018. Vol. 21. No. 3. P. 654–671.
Romashchenko M., Bohaienko V., Bilobrova A. Two-dimensional mathematical modelling of soil water regime under drip irrigation (in Ukrainian). Bulletin of Agricultural Science. 2021. Vol. 99. No. 4. P. 59–66.
Gomez-Aguilar J. F., Miranda-Hernandez M., Lopez-Lopez M. G., Alvarado-Martinez V. M., Baleanu D. Modeling and simulation of the fractional space-time diffusion equation. Communications in Nonlinear Science and Numerical Simulation. 2016, Vol. 30. P. 115–127.
van Genuchten M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.. 1980. Vol. 44. P. 886–900.
Averyanov S. F. Filtration from canals and its influence on groundwater regime (in Russian). Moscow: Kolos, 1982.
Samarskii A. A. The theory of difference schemes. New York (NY): CRC Press, 2001.
Freund R. W. A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems. SIAM J. Sci. Comput.1993. Vol. 14. No. 2. P. 470–482