Numerical solutions for 2D unsteady Laplace-type problems of anisotropic functionally graded materials

• Published in: Mathematical modelling and analysis Vol. 27; no. 2; pp. 303 - 321
• Main Author: Azis, Mohammad Ivan
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 27.04.2022
• Subjects: anisotropic Laplace-type equation; Anisotropy; Boundary element method; Boundary integral method; Coefficients; Functionally gradient materials; Inhomogeneous media; Integral equations; Laplace transform; Laplace transforms; Time dependence; variable coefficients; Iran; anisotropic Laplace-type equation; boundary element method; variable coefficients; Laplace transform
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2022.14463

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.