Search results

This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem.

The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P₁b-P₁-P₁) and solve a linear approximation based on a higher-order element pair (P₂-P₁-P₂) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible magnetohydrodynamic equations.

The algorithm uses a lower-order element pair to compute an initial approximation by the Oseen-type iteration and uses a higher-order element pair to solve a linear system in each processor.

Besides, the convergence analysis of local parallel finite element algorithm is given. Finally, numerical experiments are presented to verify the efficiency of the proposed algorithm.

Compared with the numerical solution of the common two-step method, this method is easy to realize and can produce a more accurate solution. And, this approach is executed in parallel, so it saves a lot of computational time.

The purpose of this paper is to design a parallel finite element (FE) algorithm based on fully overlapping domain decomposition for solving the nonstationary incompressible magnetohydrodynamics (MHD).

The fully discrete Euler implicit/explicit FE subproblems, which are defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain, are solved in parallel. In each subproblem, the linear term is treated by implicit scheme and the nonlinear term is solved by explicit one.

For the algorithm, the almost unconditional convergence with optimal orders is validated by numerical tests. Some interesting phenomena are presented.

The proposed algorithm is effective, easy to realize with low communication costs and preferred for solving the strong nonlinear MHD system.

The purpose of this paper is to develop a concurrent multiscale computational method for granular materials in the quasi-static loading regime.

Overlapped-coupling between a micropolar linear elastic one-dimensional (1D) mixed finite element (FE) model and a 1D chain of Hertzian nonlinear elastic, glued, discrete element (DE) spheres is presented. The 1D micropolar FEs and 1D chain of DEs are coupled using a bridging-scale decomposition for static analysis.

It was found that an open-window DE domain may be coupled to a micropolar continuum FE domain via an overlapping region within the bridging-scale decomposition formulation for statics. Allowing the micropolar continuum FE energy in the overlapping region to contribute to the DE energy has a smoothing effect on the DE response, especially for the rotational degrees of freedom (dofs).

The paper focusses on 1D examples, with elastic, glued, DE spheres, and a linear elastic micropolar continuum implemented in 1D.

A concurrent computational multiscale method for granular materials with open-window DE resolution of the large shearing region such as at the interface with a penetrometer skin, will allow more efficient computations by reducing the more costly DE domain calculations, but not at the expense of generating artificial boundary effects between the DE and FE domains.

Open-window DE overlapped-coupling to FE continuum domain, accounting for rotational dofs in both DE and FE methods. Contribution of energy from micropolar FE in overlap region to underlying DE particle energy.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

In this paper, a parallel preconditioning technique based on the additive variant of overlapping domain decomposition is described and implemented to solve magnetostatic field problems. This technique involves covering the domain with a number of overlapping subdomains. The pre‐conditioner results from adding together approximate inversions on the subdomains, Theoretical estimates for the rate of convergence for the resulting algorithm are available and are based on the properties of underlying differential equations. Numerical experiments are given to demonstrate the effectiveness of this algorithm.

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer.

The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder.

The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations.

In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented. The formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee the load balancing. Furthermore, each subdomain is assigned to a processor of a parallel computer and treated as a sub‐finite element system with information exchanged through the interface between two adjacent subdomains. With this new algorithm, these sub‐finite element systems are solved fully parallelly as independent finite element systems, not only the computations of the interior nodes but also the computations of the interface nodes can be executed parallelly. Also, the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes. An implementation of this new scheme on an iPSC/2 D5 Hypercube Concurrent Computer reached an efficiency of more than 100% when compared with the sequential SOR scheme.

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed.

The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid.

The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method.

The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.