Premium
A finite element Laplace transform solution technique for the wave equation
Author(s) -
Aral Mustafa M.,
Gülçat Ülgen
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111107
Subject(s) - laplace transform , finite element method , laplace transform applied to differential equations , laplace's equation , mathematical analysis , method of fundamental solutions , inverse laplace transform , extended finite element method , green's function for the three variable laplace equation , mathematics , wave equation , two sided laplace transform , partial differential equation , mixed finite element method , boundary value problem , inversion (geology) , boundary element method , boundary knot method , physics , fourier transform , fourier analysis , fractional fourier transform , thermodynamics , paleontology , structural basin , biology
A technique is described for the solution of the wave equation with time dependent boundary conditions. The finite element solution accompanied by the numerical Laplace inversion process seems to be an efficient procedure to treat such problems. The programming involved is straightforward in the sense that numerical Laplace inversion routines can be directly used as a time integration procedure after obtaining standard finite element differential equation solutions in the transformed domain. Some results are presented for one‐ and two‐ dimensional applications, such as wave propagation in longitudinal bars and wave propagation in harbours.