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  "body": "\n## Summary\n\nDomain decomposition methods solve a [[boundary value problem|TM8VQJWGHZ]] on a domain by splitting the domain into smaller subdomains.\nThey solve problems on the subdomains, often in parallel, and couple the local solutions through the interfaces until they fit together.\nThey are mainly used as [[preconditioners|KE98SW3SBD]] for Krylov methods on large parallel computers.\n\n## Explanations\n\n### L1 human\n\nA big problem on a complicated region is hard to solve at once.\nCut the region into pieces, give each piece to a different processor, and solve each small problem there.\nThe pieces then exchange information along their common boundaries and solve again, until the pieces agree.\nThe classical example, due to Schwarz, solves a problem on the union of a disc and a rectangle by alternating between the two shapes.\n",
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