Open AccessNUMERICAL SOLUTIONS FOR 2D UNSTEADY LAPLACE-TYPE PROBLEMS OF ANISOTROPIC FUNCTIONALLY GRADED MATERIALS
Author(s) -
Mohammad Ivan Azis
Publication year - 2022
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2022.14463
Subject(s) - mathematics , laplace transform , mathematical analysis , laplace's equation , laplace transform applied to differential equations , green's function for the three variable laplace equation , boundary element method , method of fundamental solutions , boundary value problem , integral equation , variable (mathematics) , inverse laplace transform , singular boundary method , boundary (topology) , finite element method , physics , thermodynamics
The time-dependent Laplace-type equation of variable coefficients for anisotropic inhomogeneous media is discussed in this paper. Numerical solutions to problems which are governed by the equation are sought by using a combined Laplace transform and boundary element method. The variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation after being Laplace transformed is then written in a boundary-only integral equation involving a time-free fundamental solution. The boundary integral equation is therefore employed to find the numerical solutions using a standard boundary element method. Finally the numerical results are inversely transformed numerically using the Stehfest formula to obtain solutions in the time variable. Some problems of anisotropic functionally graded media are considered. The results show that the combined Laplace transform and boundary element method is accurate and easy to implement.