An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. (English) Zbl 1429.35184
Summary: In this article, an optimizing reduced finite difference scheme (FDS) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) for the chemical vapor deposit (CVD) equations is presented. And the error estimates between the usual finite difference solution and the reduced POD solution of optimizing FDS are derived. At last, some examples of numerical simulation are given to demonstrate the consistency of the numerical and theoretical results. It is shown that the optimizing reduced FDS based on POD method is of great feasibility and efficiency.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
chemical vapor deposit equations; finite difference scheme; singular value decomposition; proper orthogonal decomposition; error estimate; numerical simulationReferences:
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