Remarks On Efficient Numerical Algorithms for Ultracomputers
Remarks On Efficient Numerical Algorithms for Ultracomputers
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These methods have been developed to extend the usefulness of fast Poisson solvers for problems on general regions. For a detailed account, we refer to O'Leary and Widlund, Math. Corap. , 1979, to appear, (also available as a DOE-NYU report, COO-30 7 7-15 5 ) . Extensive theoretical and experimental evidence shows that iterative versions of this algorithm converge in a moderate number of steps which grows only in proportion to the loga- rithm of the number of degrees of freedom.
In each step a ...fast Poisson solver is used once or twice on a simple region in which the region of interest is imbed- ded. In addition a few sparse matrix operations are carried -3- out. Some of these can be described as the creation of a three dimensional array which is zero except at mesh points close to the boundary. At these exceptional points, values are obtained by using a few arithmetic operations on data obtained from neighboring mesh points. These data can easily be accessed using the shuffle connection and the fundamental shuffle permutation in a way quite similar to that outlined in the previous section.
What to read after Remarks On Efficient Numerical Algorithms for Ultracomputers?
You can find similar books in the "Read Also" column, or choose other free books by Charles S Peskin to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
These methods have been developed to extend the usefulness of fast Poisson solvers for problems on general regions. For a detailed account, we refer to O'Leary and Widlund, Math. Corap. , 1979, to appear, (also available as a DOE-NYU report, COO-30 7 7-15 5 ) . Extensive theoretical and experimental evidence shows that iterative versions of this algorithm converge in a moderate number of steps which grows only in proportion to the loga- rithm of the number of degrees of freedom.
In each step a ...fast Poisson solver is used once or twice on a simple region in which the region of interest is imbed- ded. In addition a few sparse matrix operations are carried -3- out. Some of these can be described as the creation of a three dimensional array which is zero except at mesh points close to the boundary. At these exceptional points, values are obtained by using a few arithmetic operations on data obtained from neighboring mesh points. These data can easily be accessed using the shuffle connection and the fundamental shuffle permutation in a way quite similar to that outlined in the previous section.
What to read after Remarks On Efficient Numerical Algorithms for Ultracomputers?
You can find similar books in the "Read Also" column, or choose other free books by Charles S Peskin to read onlineMoreLess
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