He, Yuanyuan; Zhu, Jialin Virtual boundary element method for 3D unsteady diffusion equations. (Chinese. English summary) Zbl 1240.65283 J. Numer. Methods Comput. Appl. 31, No. 2, 99-107 (2010). Summary: Based on the virtual boundary element method (VBEM) for potential theory and time-dependent fundamental solution of diffusion equations, an implementation of the VBEM-collation method for 3D unsteady diffusion equations is proposed. The VBEM not only retains the advantages of the boundary element method, but also avoids singular integration or nearly singular integration. High accuracy and efficiency are observed just with a small number of boundary elements in the method. Several test problems are examined, and the results are in excellent agreement with available analytical solutions. In addition, the choosing range of the distance between the real boundary and the virtual boundary is investigated, which is narrower than that of VBEM applied in elliptic problems. MSC: 65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:virtual boundary element method; collocation method; single layer potential; unsteady diffusion equation; numerical examples PDFBibTeX XMLCite \textit{Y. He} and \textit{J. Zhu}, J. Numer. Methods Comput. Appl. 31, No. 2, 99--107 (2010; Zbl 1240.65283)