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- W2034244672 abstract "Standard numerical methods for the heat equation in two or more space dimensions are excellent if it is necessary to follow the evolution in great detail through many small timesteps. This paper presents efficient and accurate new adaptive methods that solve the free-space heat equation with large timesteps. These methods combine the fast Gauss transform with an adaptive refinement scheme that represents the solution as a continuous piecewise polynomial, to a user-specified degree of accuracy. The same approach is extended to solve inhomogeneous problems and to solve the heat equation in moving domains with boundaries. In problems with boundaries, it allows the use of accurate boundary representations without requiring difficult product integration formulas or precluding fast evaluation schemes. Numerical experiments in two space dimensions show these methods to be accurate and efficient, especially for highly nonuniform or discontinuous initial data or when substantial accuracy is required." @default.
- W2034244672 created "2016-06-24" @default.
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- W2034244672 date "1994-01-01" @default.
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- W2034244672 title "Fast Adaptive Methods for the Free-Space Heat Equation" @default.
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- W2034244672 doi "https://doi.org/10.1137/0915013" @default.
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