Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds

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FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple ... continued below

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Wiegmann, A. June 1, 1999.

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FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.

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  • Report No.: LBNL-43565
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/982430 | External Link
  • Office of Scientific & Technical Information Report Number: 982430
  • Archival Resource Key: ark:/67531/metadc1014521

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  • June 1, 1999

Added to The UNT Digital Library

  • Oct. 14, 2017, 8:36 a.m.

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  • Oct. 17, 2017, 6:12 p.m.

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Wiegmann, A. Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds, report, June 1, 1999; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1014521/: accessed December 14, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.