Parallel Finite Element Method Research Articles

Parallel FEM for structural analysis of reinforced systems

Calculations in software systems based on the finite element method (FEM), performed with account for genetic nonlinearity, i.e., assembling, are not feasible for a number of construction problems. In particular, in buildings made of factory-made and cast-in-place concrete, the latter is gradually involved in deformation and external load processes. In reconstructed buildings, during the increase in the element cross-section (e.g., reinforced concrete or metal casing), the reinforcing and reinforced materials are also involved in deformation and external load processes at different time. As a result, there are initial stresses and strains in the "old" part of the element by the time its "new" part installation and strength gain. At the same time, in the reinforcing material or cast-in-place element, the stress-strain state is zero until the additional load is applied.Thus, during the structural analysis, a change in the finite element stiffness is required. But FEM software systems have no finite element capable of changing (increasing) the stiffness. This determines the relevance of the developed algorithm for the structural analysis of factory-made and cast-in-place concrete buildings using the parallel FEM.Purpose: The aim of this work is to improve the parallel FEM and develop a calculation algorithm based on it.Research findings: Based on the parallel FEM, the calculation algorithm is proposed for factory-made and cast-in-place concrete buildings. The proposed algorithm accounts for the structural properties of such buildings, including the gradual involvement of different-aged materials in the deformation process. Using the proposed algorithm, the structural analysis is conducted for the reconstructed system, in which the finite element is replaced by the parallel element, and the hinge coupling of elements is simultaneously replaced by a rigid one.

Improved parallel finite element methods for the stationary Navier–Stokes problem

Improved parallel finite element methods for the stationary Navier–Stokes problem

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in practical room acoustics. The implementation is benchmarked on heterogeneous multi-device many-core computing architectures, and high performance and scalability are demonstrated for a problem that is considered expensive to solve in practical applications. In a benchmark study, scaling tests show that multi-GPU support gives the ability to simulate large rooms, over a broad frequency range, with realistic boundary conditions, both in terms of computing time and memory requirements. Furthermore, numerical simulations on two non-trivial geometries are presented, a star-shaped room with a dome and an auditorium. Overall, this shows the viability of using a multi-device accelerated DGFEM solver to enable realistic large-scale wave-based room acoustics simulations.

A parallel finite element method based on fully overlapping domain decomposition for the steady-state Smagorinsky model

A parallel finite element method based on fully overlapping domain decomposition for the steady-state Smagorinsky model

Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition

Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition

Parallel Iterative FEM Solver with Initial Guess for Frequency Domain Electromagnetic Analysis

The finite element method is a key player in computational electromagnetics for designing RF (Radio Frequency) components such as waveguides. The frequency-domain analysis is fundamental to identify the characteristics of the components. For the conventional frequency-domain electromagnetic analysis using FEM (Finite Element Method), the system matrix is complex-numbered as well as indefinite. The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps. However, such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver. It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency. Overall, it is hard to adopt conventional iterative solvers even though the system matrix is sparse. A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper. In this implementation, the previous solution of the iterative solver of Matlab (Matrix Laboratory) employing the preconditioner is used for the initial guess for the next step’s solution process. The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting, which ruins the convergence of early steps in each parallel stage. Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.

A modified local and parallel finite element method for the coupled Stokes-Darcy model with the Beavers-Joseph interface condition

A modified local and parallel finite element method for the coupled Stokes-Darcy model with the Beavers-Joseph interface condition

Local and Parallel Finite Element Methods Based on Two-grid Discretizations for a Transient Coupled Navier-Stokes/Darcy Model

Local and Parallel Finite Element Methods Based on Two-grid Discretizations for a Transient Coupled Navier-Stokes/Darcy Model

Parallel Domain Decomposition of a FEM-based Tool for Numerical Modelling Mineral Slurry-like Flows

The main parallelisation related features of a computational tool based on the finite element method (FEM) for the numerical modelling of mineral-slurry like flows are described in this work. In particular, both the domain decomposition method (DDM) and the processes communication strategy employed are discussed in detail. The DD algorithm is based on the iterative update of the boundary conditions imposed on the interfaces between subdomains, the so-called transmission conditions. Due to its versatility in several parallel architectures, the message-passing standard used here is the message passing interface (MPI) one. Since mineral-slurries rheology may change according to the prevailing local flow conditions, Newtonian and non-Newtonian viscous fluids are considered in this work. Indeed, both Newtonian and non-Newtonian laminar flows are numerically studied in two well-known canonical configurations usually found in mineral-slurry transport. The main results show that the parallel FEM based tool is capable of carrying out high-fidelity numerical simulations of mineral-slurry like flows. Finally, in all numerical simulations performed, relatively good speedups were obtained.

Local and parallel finite element methods based on two-grid discretizations for a non-stationary coupled Stokes-Darcy model

In this paper, some local and parallel finite element methods based on two-grid discretizations are proposed and investigated for a non-stationary coupled Stokes-Darcy model. Based on two-grid discretizations, a semi-discrete scheme is presented. With backward Euler scheme for the temporal discretization and two-grid discretizations for the spatial discretization, some fully discrete schemes are proposed. The crucial idea is to adopt a decoupling scheme based on interface approximation via temporal extrapolation to approximate the mixed model by utilizing a coarse grid on the whole domain, then solve some residual equations with a finer grid on some overlapped subdomains by some local and parallel procedures at each time step. The interface coupling term on the subdomains with fine grid is approximated by the coarse-grid approximations. To reach a global continuous approximation, a new parallel algorithm based on the partition of unity is devised. Some local a priori estimate that is crucial for the theoretical analysis is obtained. Finally, some numerical experiments are conducted to support our theoretical results and demonstrate the computational effectiveness.

Predictive Simulation for Surface Fault Occurrence Using High-Performance Computing

Numerical simulations based on continuum mechanics are promising methods for the estimation of surface fault displacements. We developed a parallel finite element method program to perform such simulations and applied the program to reproduce the 2016 Kumamoto earthquake, where surface rupture was observed. We constructed an analysis model of the 5 × 5 × 1 km domain, including primary and secondary faults, and inputted the slip distribution of the primary fault, which was obtained through inversion analysis and the elastic theory of dislocation. The simulated slips on the surface were in good agreement with the observations. We then conducted a predictive simulation by inputting the slip distributions of the primary fault, which were determined using a strong ground motion prediction method for an earthquake with a specified source fault. In this simulation, no surface slip was induced in the sub-faults. A large surface slip area must be established near a sub-fault to induce the occurrence of a slip on the surface.

A New Local and Parallel Finite Element Method for the Coupled Stokes–Darcy Model

A New Local and Parallel Finite Element Method for the Coupled Stokes–Darcy Model

A novel multiscale parallel finite element method for the study of the hygrothermal aging effect on the composite materials

In this paper, a novel and comprehensive multiscale finite element analysis is proposed to study the effect of hygrothermal aging on the behavior of fiber-reinforced composite materials. The temperature dependence of the material diffusivity and its spatial variation are considered. Fick's equation is numerically solved by the finite-difference approach and problems in which the temperature and/or humidity are different at the material boundaries are studied. In addition to the elastic properties degradation, the change of the coefficients of thermal and moisture expansion and the effect of the glass transition temperature in the hygrothermal aging process are considered. The algorithm has been used to study the time-dependent (transient) behavior of two sample laminated composites with different types of temperature and humidity boundary conditions. The maximum decline of about 87% and 74% has been observed in the transverse Young's modulus and shear modulus of the composite in the thickness direction. Furthermore, the coefficients of the thermal and moisture transverse expansion have been found to change from initial values of 0.12 and 7.31μmm°C to 0.45 and 7.96μmm°C in some hygrothermal conditions. The developed algorithm is applicable to a wide variety of composite materials and structures.

Development of a general‐purpose parallel finite element method for analyzing earthquake engineering problems

AbstractA parallel finite element method (FEM) based on high‐fidelity models for solving diverse earthquake engineering problems is presented. Its key feature is a parallel solver that is tuned to solve large‐scale wave equations. Tensorial material constitutive relations of concrete and soil and sophisticated nonlinear joint elements are implemented to broaden the applicability of the parallel FEM. The performance of the proposed parallel FEM is demonstrated for three examples; namely, seismic response, liquefaction, and surface earthquake fault analyses. A high‐fidelity model was constructed for each analysis, and the numerical results were validated against observed data. The performance of the proposed parallel FEM approach was evaluated in terms of the resolution of the simulated results. Ensemble computing based on approximately a hundred high‐fidelity models is useful for cases where there are considerable uncertainties regarding the material properties.

Analysis of the local and parallel space-time algorithm for the heat equation

In this paper, a second-order local and parallel space-time algorithm is proposed and analyzed for the heat equation. This scheme is based on the parareal with spectral deferred correction method in time and the expandable local and parallel finite element method in space. It realizes the parallelism both in the temporal as well as in the spatial direction. We prove its stability and the optimal error estimation in L2-norm. At last, several numerical experiments are presented to demonstrate the effectiveness of our parallel scheme.

Local and parallel finite element methods based on two‐grid discretizations for unsteady convection–diffusion problem

AbstractIn this article, some local and parallel finite element methods are proposed and investigated for the time‐dependent convection–diffusion problem. With backward Euler scheme for the temporal discretization, the basic idea of the present methods is that for a solution to the considered equations, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure at each time step. The partition of unity is used to collect the local high frequency components to assemble a global continuous approximation. Theoretical results are obtained and numerical tests are reported to support the theoretical findings.

Comparison of Parallel-in-Space-and-Time Finite-Element Methods for Magnetic Field Analysis of Electric Machines

This article investigates the effectiveness of two parallel-in-space-and-time (PinST) finite-element methods (FEMs) in magnetic field analyses of practical electric machines. A combination of an ordinary domain decomposition method (DDM) with a parallel time-periodic FEM is compared with a PinST FEM based on the DDM combined with a parallel time-periodic explicit-error-correction method. To clarify and compare the performances of the two methods in terms of their parallel efficiencies, numerical results of an interior permanent magnet synchronous motor are presented.

A novel local and parallel finite element method for the mixed Navier–Stokes–Darcy problem

In this paper, based on two-grid discretization, a new local and parallel finite element method is proposed and investigated for the mixed Navier–Stokes–Darcy problem. Compared with the classical local and parallel finite element method, the main features of our method are: (1) partition of unity method is considered to generate local subproblems; (2) global continuous approximations are achieved. We theoretically analyze the proposed method and report on some numerical tests to support the theoretical results.

Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations

In this paper, some local and parallel finite element methods based on two-grid discretizations are proposed and investigated for the unsteady Navier-Stokes equations. The backward Euler scheme is considered for the temporal discretization, and two-grid method is used for the space discretization. The key idea is that for a solution to the unsteady Navier-Stokes problem, we could use a relatively coarse mesh to approximate low-frequency components and use some local fine mesh to compute high-frequency components. Some local a priori estimate is obtained. With that, theoretical results are derived. Finally, some numerical results are reported to support the theoretical findings.

An Efficient Parallel Hybrid Method of FEM-MLFMA for Electromagnetic Radiation and Scattering Analysis of Separated Objects

In order to meet the rapidly increasing demand for accurate and efficient analysis of complex radiating or scattering structures in the presence of electrically large objects, a finite element method (FEM)-multilevel fast multipole algorithm (MLFMA) hybrid method that based on the Finite Element-Iterative Integral Equation Evaluation (FE-IIEE) mesh truncation technique is proposed in this paper. The present method makes use of FEM for the regions with small and complex features and MLFMA for the analysis of the electrically large objects, which ensure the accuracy and applicability of the method are better than most commonly adopted FEM-high frequency technique (HFT) hybrid method. The mutual interactions between regions are taken into account in a fully coupled way through iterative near filed computation process. In order to achieve an excellent performance, both algorithms have been implemented together from scratch, being able to run over multi CPU cores. An efficient parallel FEM domain decomposition method (DDM) solver with exploiting geometrical repetitions is included to drastically reduce memory requirements and computational time in the calculation of large array antenna. Also, the parallel MLFMA is adopted to expedite the near-field information exchange between regions. Through numerical example, the effect of distance between regions on the convergence of the proposed hybrid method is studied, and it is shown that the proposed method converge well even if the distance is equal to 0.05λ. Through comparisons with an in-house higher order method of moments (HOMoM) code and commercial software FEKO, the accuracy and effectiveness of the implemented parallel hybrid method are validated showing excellent performance.