| SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS |
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| 引用本文： | 金小庆. SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS[J]. 高等学校计算数学学报(英文版), 1993, 0(1) |
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| 作者姓名： | 金小庆 |
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| 作者单位： | Faculty of |
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| 摘 要： | In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.
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SINE TRANSFORM PRECONDITIONERS FOR SECOND -ORDER PARTIAL DIFFERENTIAL EQUATIONS |
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| Jin Xiao-qing Faculty of Science and Technology,University of Macau,Macau.. SINE TRANSFORM PRECONDITIONERS FOR SECOND -ORDER PARTIAL DIFFERENTIAL EQUATIONS[J]. Numerical Mathematics A Journal of Chinese Universities English Series, 1993, 0(1) |
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| Authors: | Jin Xiao-qing Faculty of Science Technology University of Macau Macau. |
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| Abstract: | In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale. |
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| Keywords: | Sine Transform finite difference method second-order partial differential equation condition number preconditioned conjugate gradient method |
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