Pasciak, Joseph E. A new scalar potential formulation of the magnetostatic field problem. (English) Zbl 0552.65082 Math. Comput. 43, 433-445 (1984). A new method for approximating magnetostatic field problems is given. The new method approximates the scalar potential for the magnetic intensity and is based on a volume integral formulation. The derivation of the new computational method uses the spectral properties of the relevant integral operator. The corresponding algorithm is similar to that obtained from coupled differential and boundary integral approaches. Convergence and stability theorems are proven. Finally, convergence results in actual computations are compared with results for the usual volume integral method used in GFUN3D. Cited in 3 Documents MSC: 65Z05 Applications to the sciences 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application 78A30 Electro- and magnetostatics Keywords:magnetostatic field problems; Convergence; stability; volume integral method PDFBibTeX XMLCite \textit{J. E. Pasciak}, Math. Comput. 43, 433--445 (1984; Zbl 0552.65082) Full Text: DOI