Fourier transform is applied to remove the time-dependent variable in the diffusion equation.Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method ...Fourier transform is applied to remove the time-dependent variable in the diffusion equation.Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method of fundamental solutions and the method of particular solutions.The particular solution of Helmholtz equation is available as shown in[4,15].The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm.Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response.Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.展开更多
基金The second author acknowledges the support of the Distinguished Overseas Visiting Scholar Fellowship funded by the Minister of Education in China and the support of NATO-RTA project under reference AVT-08/1.
文摘Fourier transform is applied to remove the time-dependent variable in the diffusion equation.Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method of fundamental solutions and the method of particular solutions.The particular solution of Helmholtz equation is available as shown in[4,15].The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm.Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response.Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.