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Sine transform based preconditioners for elliptic problems (1997)

Chan, Raymond H. ; Wong, C. K.

New York, NY [u.a.] : Wiley-Blackwell

Numerical Linear Algebra with Applications 4 (1997), S. 351-368

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ISSN: 1070-5325

Schlagwort(e): sine transform ; preconditioned conjugate gradient method ; elliptic partial differential equation ; Engineering ; Numerical Methods and Modeling

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: We consider applying the preconditioned conjugate gradient (PCG) method to solving linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators with Dirichlet boundary conditions. Let (L + Σ)Σ-1(Lt + Σ) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix Σ. We propose a preconditioner M = (L^ + Σ^)Σ^-1(L^t + Σ^) with block diagonal matrix Σ^ and lower block triangular matrix L^. The diagonal blocks of Σ^ and the subdiagonal blocks of L^ are respectively the optimal sine transform approximations to the diagonal blocks of Σ and the subdiagonal blocks of L. We show that for two-dimensional domains, the construction cost of M and the cost for each iteration of the PCG algorithm are of order O(n2 log n). Furthermore, for rectangular regions, we show that the condition number of the preconditioned system M-1A is of order O(1). In contrast, the system preconditioned by the MILU and MINV methods are of order O(n). We will also show that M can be obtained from A by taking the optimal sine transform approximations of each sub-block of A. Thus, the construction of M is similar to that of Level-1 circulant preconditioners. Our numerical results on two-dimensional square and L-shaped domains show that our method converges faster than the MILU and MINV methods. Extension to higher-dimensional domains will also be discussed. © 1997 John Wiley & Sons, Ltd.

Zusätzliches Material: 1 Ill.

Materialart: Digitale Medien

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Digitale Medien

PERFORMANCE PREDICTION OF A BACKSWEPT CENTRIFUGAL IMPELLER AT OFF-DESIGN POINT CONDITIONS (1996)

ZHANG, MOU-JIN ; POMFRET, M. J. ; WONG, C. M.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 23 (1996), S. 883-895

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ISSN: 0271-2091

Schlagwort(e): N-S solver ; Turbomachinery ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Maschinenbau

Notizen: The internal flows inside a backswept centrifugal impeller at off-design point conditions are analysed by solving the fully three- dimensional Navier-Stokes equations coupled with the k-∊ two-equation turbulence model. Conditions analysed have flow rates of 85 per cent and 113 per cent of the design rate. The calculated results are compared with published experimental data and the comparison shows good agreement. A jet wake structure occurs near the outlet of the impeller for each of the two off-design flow rates and the location and size of the jet wake structure seem to be independent of the flow rate.

Zusätzliches Material: 13 Ill.

Materialart: Digitale Medien

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A network method for nonlinear transient eddy current problems (1987)

Wong, C. C.

New York, NY [u.a.] : Wiley-Blackwell

Communications in Applied Numerical Methods 3 (1987), S. 39-48

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ISSN: 0748-8025

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: Maxwell's curl equations for a conducting region are simulated by the impedance network. A set of simultaneous first-order ordinary differential equations is developed for the network which can be used to solve linear or nonlinear, transient or static eddy current problems. The resulting set of equations is solved by the explicit fourth order Runge-Kutta method and in some cases by an implicit method based on the central difference scheme for time discretization. A number of examples, including eddy current losses in a saturated steel plate, are described to illustrate the applications of the method. It is found that the explicit method is more suitable for nonlinear problems, whereas the implicit method is more efficient for linear problems.

Zusätzliches Material: 5 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/cnm.1630030108

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