Topic
Laplace's equation
About: Laplace's equation is a research topic. Over the lifetime, 7088 publications have been published within this topic receiving 132118 citations. The topic is also known as: Laplace equation & Laplace's PDE.
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TL;DR: First the freefem++ software deals with mesh adaptation for problems in two and three dimension, second, it solves numerically a problem with phase change and natural convection, and finally to show the possibilities for HPC the software solves a Laplace equation by a Schwarz domain decomposition problem on parallel computer.
Abstract: This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.
2,867 citations
2,605 citations
Book•
01 Jan 2000
TL;DR: In this article, the Laplace equation, the Helmholtz equation, and the Sobolev spaces of strongly elliptic systems have been studied and further properties of spherical harmonics have been discussed.
Abstract: Introduction 1. Abstract linear equations 2. Sobolev spaces 3. Strongly elliptic systems 4. Homogeneous distributions 5. Surface potentials 6. Boundary integral equations 7. The Laplace equation 8. The Helmholtz equation 9. Linear elasticity Appendix A. Extension operators for Sobolev spaces Appendix B. Interpolation spaces Appendix C. Further properties of spherical harmonics Index of notation Index.
2,450 citations
TL;DR: The Fokker-Planck Equation: Methods of Solution and Applications as discussed by the authors is a well-known method for solution and application in the field of Optica-Acta.
Abstract: (1984). The Fokker-Planck Equation: Methods of Solution and Applications. Optica Acta: International Journal of Optics: Vol. 31, No. 11, pp. 1206-1207.
1,541 citations
TL;DR: An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory using CPUs proportional to n.
1,426 citations