DBEM solutions to modified Helmholtz problems for FGMs of space–time-dependent properties

Abstract

A combined Laplace transform (LT) and domain-boundary element method (DBEM) are utilized to obtain numerical solutions for a spatio-temporal coefficient modified Helmholtz-type equation with arbitrary initial conditions and source terms, addressing problems in a distinct class of anisotropic functionally graded materials (FGMs). The process involves deriving a domain-boundary integral equation by transforming the variable coefficient equation into a constant coefficient equation and applying the Laplace transform. Numerical solutions are then obtained using the standard domain-boundary element method and the Stehfest formula. This study demonstrated the accuracy of numerical solutions.

Keywords

• Anisotropic functionally graded materials
• Variable coefficients
• Modified Helmholtz-type equation
• Laplace transform
• Domain-boundary element method