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| Solution of Helmholtz equation by differential cubature method |
| Revised:June 10, 2001 |
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| DOI：10.7511/jslx20032045 |
| KeyWord:Helmholtz equation,numerical solution technique,differential cubature method |
| Wu Lanhe \ Li Chunyu |
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| Abstract: |
| A novel numerical solution technique, the differential cubature method is employed to solve the two\|dimensional Helmholtz equations. The basic idea of the differential cubature method is to express a linear differential operation such as a continuous function or any orders of partial derivatives of a multivariable function, or combinations of them as a weighted linear sum of the discrete function values chosen within the overall domain of a problem. The weighting coefficients can be obtained by chosing a set of monomials as the trial functions. By using the differential cubature procedure, the governing differential equations and boundary conditions are transformed into a set of linear algebraic equations of the function values at the each discrete point. The convergency, accuracy and applicability of this method are demonstrated through solving some sample problems of the different wave numbers, which have exact solutions. It was found that this method is more suitable for solving the Helmholtz equations of lower wave numbers. |
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