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  "body": "\n## Summary\n\nThe method of fundamental solutions approximates the solution of a linear homogeneous elliptic equation by a sum of [[fundamental solutions|K2NK9A8M5F]].\nThese are centred at source points outside the domain.\nEach term solves the equation exactly inside the domain, so only the boundary condition has to be fitted.\nIt needs neither a mesh nor integrals, only the evaluation of the fundamental solution at boundary points.\nIt is used when the fundamental solution is known in closed form.\nExamples are the Laplace equation $\\Delta u = 0$, with $\\Delta$ the [[Laplacian|0E0B6RA8K0]], the [[Helmholtz equation|MNXKTXJ35G]], and linear elasticity.\nSee the [[definition|XS0Q09SV2T]].\n\n## Explanations\n\n### L1 human\n\nPlace a few point charges outside a region.\nThe electric potential they create satisfies the Laplace equation everywhere inside the region.\nBy choosing the strengths of the charges well, one can make this potential match given values on the boundary of the region, at least approximately.\nThe method of fundamental solutions does exactly this, and the resulting sum of charge potentials is the approximate solution.\n",
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