An efficient extrapolation full multigrid method for elliptic problems in two and three dimensions

In recent three decades, the finite element method (FEM) has rapidly developed as an important numerical method and used widely to solve large-scale scientific and engineering problems. In the fields of structural mechanics such as civil engineering , automobile industry and aerospace industry, the finite element method has successfully solved many engineering practical problems, and it has penetrated almost every field of today's sciences and engineering, such as material science, electricmagnetic fields, fluid dynamics, biology, etc. In this paper, we will overview and summarize the development of the p and h-p version finite element method, and introduce some recent new development and our newest research results of the p and h-p version finite element method with quasi-uniform meshes in three dimensions for elliptic problems.

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Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method

Journal of Turbomachinery ◽

10.1115/1.2929430 ◽

1994 ◽

Vol 116 (3) ◽

pp. 435-445 ◽

Cited By ~ 126

Author(s):

A. Arnone

Keyword(s):

Multigrid Method ◽

Flow Analysis ◽

Three Dimensional ◽

Maximum Flow ◽

Variable Coefficients ◽

Rotating Blade ◽

A Cell ◽

Space Discretization ◽

Transonic Fan ◽

Full Multigrid Method

A three-dimensional code for rotating blade-row flow analysis has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling for the artificial dissipation. The computational efficiency of a four-stage Runge–Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, nonperiodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

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PERFORMANCE IMPROVEMENT OF FLOW COMPUTATIONS WITH AN OVERSET-GRID METHOD INCLUDING BODY MOTIONS USING A FULL MULTIGRID METHOD

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016) ◽

10.7712/100016.2338.6872 ◽

2016 ◽

Cited By ~ 1

Author(s):

Kunihide Ohashi ◽

Hiroshi Kobayashi

Keyword(s):

Performance Improvement ◽

Multigrid Method ◽

Grid Method ◽

Overset Grid ◽

Overset Grid Method ◽

Full Multigrid Method

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High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

Mathematical Problems in Engineering ◽

10.1155/2018/7831731 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Yan Wang ◽

Yongbin Ge

Keyword(s):

Difference Scheme ◽

Multigrid Method ◽

Elliptic Problems ◽

High Order ◽

Compact Difference Scheme ◽

Central Difference ◽

Present Scheme ◽

Compact Difference ◽

Compact Approximations ◽

Error Terms

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

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