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1.
    
We present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound‐hard scatterer. We apply this method to the solution of a mock‐up submarine problem, and highlight its computational advantages and intrinsic parallelism. A key component of our method is an original idea for addressing a Neumann boundary condition in the general framework of a fictitious domain method. This idea is applicable to many other linear partial differential equations besides the Helmholtz equation. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

2.
    
This paper presents an examination of moving‐boundary temperature control problems. With a moving‐boundary problem, a finite‐element mesh is generated at each time step to express the position of the boundary. On the other hand, if an overlapped domain, that is, comprising foreground and background meshes, is prepared, the moving boundary problem can be solved without mesh generation at each time step by using the fictitious domain method. In this study, boundary temperature control problems with a moving boundary are formulated using the finite element, the adjoint variable, and the fictitious domain methods, and several numerical experiments are carried out. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

3.
    
The finite cell method (FCM) combines the fictitious domain approach with the p‐version of the finite element method and adaptive integration. For problems of linear elasticity, it offers high convergence rates and simple mesh generation, irrespective of the geometric complexity involved. This article presents the integration of the FCM into the framework of nonlinear finite element technology. However, the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map. As a consequence of the weak penalization, nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries, leading to a low algebraic rate of convergence. Therefore, the FCM approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp‐d method, which synergetically uses the h‐adaptivity of the integration scheme. Numerical experiments show that the hp‐d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map. The hp‐d‐adaptive FCM is thus able to restore high convergence rates for the geometrically nonlinear case, while preserving the easy meshing property of the original FCM. Accuracy and performance of the present scheme are demonstrated by several benchmark problems in one, two, and three dimensions and the nonlinear simulation of a complex foam sample. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

4.
This contribution presents a numerical strategy to evaluate the effective properties of image‐based microstructures in the case of random material properties. The method relies on three points: (1) a high‐order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model‐reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
    
This paper describes a parallel finite‐element system implemented using the domain decomposition method on a cluster of remote computers connected via the Internet. This technique is also readily applicable to a grid computing environment. A three‐dimensional finite‐element elastic analysis involving more than one million degrees of freedom was solved using this system, and a good approximate solution was obtained with high parallel efficiency of over 90% using remote computers located in three different countries. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

6.
有限元并行计算中网格自动区域划分的研究   总被引：6，自引：0，他引：6       下载免费PDF全文
本文针对集群系统下大规模并行有限元分析,设计了简单实用的网格自动区域划分算法,以使并行计算时减少由于负载不均衡所引起的效率下降,并应用于“汽车碰撞模拟”项目中的车架模型的分割。重点讨论并改进了贪婪算法和ANP算法,并比较了两种算法各自的特点及其适用性。通过数值算例证明,对于不同类型的有限元网格都得到了满意的结果,本文的算法具有广泛的适用性。且对该算法稍加改进,则可应用于各类动态并行计算问题所提出的动态负载均衡要求。  相似文献   

7.
    
We report on a generalization of the Bayliss–Gunzburger–Turkel non‐reflecting boundary conditions to arbitrarily shaped convex artificial boundaries. For elongated scatterers such as submarines, we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three‐dimensional acoustic scattering problems. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

8.
    
The finite cell method is a fictitious domain approach based on hierarchical Ansatz spaces of higher order. The method avoids time‐consuming and often error‐prone mesh‐generation and favorably exploits Cartesian grids to embed structures of complex geometry in a simple‐shaped computational domain thus shifting parts of the computational effort from mesh generation to the computation within the embedding finite cells of regular shape. This paper presents an effective integration approach for voxel‐based models of linear elasticity that drastically reduces the computational effort on cell level. The applied strategy allows the pre‐computation of an essential part of the cell matrices and vectors of higher order, representing stiffness and load, respectively. Several benchmark problems show the potential of the proposed method in particular for heterogeneous material properties as common in biomedical applications based on computer tomography scans. The applied strategy ensures a fast computation for time‐critical simulations and even allows user‐interactive simulations for models of moderate size at a high level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
    
An extension of the FETI‐H method is designed for the solution of acoustic scattering problems with multiple right‐hand sides. A new local pre‐conditioning of this domain decomposition method is also presented. The potential of the resulting iterative solver is demonstrated by numerical experiments for two‐dimensional problems with high wavenumbers, as many as 2.5 million complex degrees of freedom, and a sweep on the angle of the incident wave. Preliminary results for a three‐dimensional submarine problem are also included. The FETI‐H method, whose numerical scalability with respect to the mesh and subdomain sizes was previously established, is shown here to be also numerically scalable with respect to the wavenumber. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

10.
    
This paper presents an algorithm for the refinement of two- or three-dimensional meshes with respect to an implicitly given domain, so that its surface is approximated by facets of the resulting polytopes. Using a Cartesian grid, the proposed algorithm may be used as a mesh generator. Initial meshes may consist of polytopes such as quadrilaterals and triangles, as well as hexahedrons, pyramids, and tetrahedrons. Given the ability to compute edge intersections with the surface of an implicitly given domain, the proposed marching volume polytopes algorithm uses predefined refinement patterns applied to individual polytopes depending on the intersection pattern of their edges. The refinement patterns take advantage of rotational symmetry. Since these patterns are applied independently to individual polytopes, the resulting mesh may encompass the so-called orientation problem, where two adjacent polytopes are rotated against one another. To allow for a repeated application of the marching volume polytopes algorithm, the proposed data structures and algorithms account for this ambiguity. A simple example illustrates the advantage of the repeated application of the proposed algorithm to approximate domains with sharp corners. Furthermore, finite element simulations for two challenging real-world problems, which require highly accurate approximations of the considered domains, demonstrate its applicability. For these simulations, a variant of the fictitious domain method is used.  相似文献   

11.
    
In this paper we present a new approach to simulations on complex‐shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ?2 and ?3. Convergence rates for different polynomial degrees are studied. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

12.
    
The use of arbitrary order edge elements for the simulation of two‐dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described. Single‐frequency incident waves, generated by a source in the far field, are considered and the solution is determined in the frequency domain. For numerical simulation, the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non‐reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer (PML). Several examples are included to demonstrate the performance of the proposed procedure. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

13.
采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。  相似文献   

14.
    
A method is presented to accelerate the execution of integral equation time domain analyses of exterior acoustic scattering problems. Conventionally, these have costs which scale with the fifth power of the frequency of the excitation, and practical limits to such computations are reached when bodies approach perhaps ∼5–10 wavelengths long. The fast approach presented is based on exploiting the pulsed nature of the illumination to omit much nugatory calculation. There is an associated slight accuracy loss; this is investigated. The method has costs which can scale with frequency to the power as low as ∼3, such that, for example, costs on a 18·5 wavelength body are reduced by a factor of about 28, with this factor itself increasing with roughly the square of the body size. Associated with the reduction in operations is a reduction in the scaling of storage required, from the third to the second power of frequency. Examples of analysis of large scatterers are presented, extending to a ∼22000 node ‘almond’. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

15.
    
This paper presents mathematical derivation of enrichment functions in the extended finite element method for numerical modeling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by one interface across which displacement field suffers a jump. The main steps towards the derivation of enrichment functions are as follows: (1) extension of the subfields separated by the interface to the whole element domain and definition of complementary nodal variables; (2) construction of characteristic functions for describing the geometry and physical field; (3) determination of the sets of basic nodal variables; (4) domain decompositions according to Step 3 and then reproduction of the physical field in terms of characteristic functions and nodal variables; and (5) comparison of the piecewise interpolations formulated at Steps 3 and 4 with the standard extended finite element method form, which yields enrichment functions. In this process, the physical meanings of both the basic and complementary nodal variables are clarified, which helps to impose Dirichlet boundary conditions. Enrichment functions for weak discontinuities are constructed from deeper insights into the structure of the functions for strong discontinuities. Relationships between the two classes of functions are naturally established. Improvements upon basic enrichment functions for weak discontinuities are performed so as to achieve satisfactory convergence and accuracy. From numerical viewpoints, a simple and efficient treatment on the issue of blending elements is also proposed with implementation details. For validation purposes, applications of the derived functions to heterogeneous problems with imperfect interfaces are presented. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

16.
    
This paper presents a (higher‐order) finite element approach for the simulation of heat diffusion and thermoelastic deformations in NC‐milling processes. The inherent continuous material removal in the process of the simulation is taken into account via continuous removal‐dependent refinements of a paraxial hexahedron base‐mesh covering a given workpiece. These refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm. The resulting mesh is used for an element‐wise defined characteristic function for the milling‐dependent workpiece within that paraxial hexahedron base‐mesh. Using this characteristic function, a (higher‐order) fictitious domain method is used to compute the heat diffusion and thermoelastic deformations, where the corresponding ansatz spaces are defined for some hexahedron‐based refinement of the base‐mesh. Numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape because of thermoelastic deformations in the process.  相似文献   

17.
This paper contains a first systematic analysis of a posteriori estimation for finite element solutions of the Helmholtz equation. In this first part, it is shown that the standard a posteriori estimates, based only on local computations, severely underestimate the exact error for the classes of wave numbers and the types of meshes employed in engineering analysis. This underestimation can be explained by observing that the standard error estimators cannot detect one component of the error, the pollution error, which is very significant at high wave numbers. Here, a rigorous analysis is carried out on a one-dimensional model problem. The analytical results for the residual estimator are illustrated and further investigated by numerical evaluation both for a residual estimator and for the ZZ-estimator based on smoothening. In the second part, reliable a posteriori estimators of the pollution error will be constructed. © 1997 by John Wiley & Sons, Ltd.  相似文献   

18.
In part I of this investigation, we proved that the standard a posteriori estimates, based only on local computations, may severely underestimate the exact error for the classes of wave-numbers and the types of meshes employed in engineering analyses. We showed that this is due to the fact that the local estimators do not measure the pollution effect inherent to the FE-solutions of Helmholtz' equation with large wavenumber. Here, we construct a posteriori estimates of the pollution error. We demonstrate that these estimates are reliable and can be used to correct the standard a posteriori error estimates in any patch of elements of interest. © 1997 John Wiley & Sons, Ltd.  相似文献   

19.
    
We present a finite element formulation for simulation of electromechanical coupling using a combination of fictitious domain and level set methods. The electric field is treated with a fixed (Eulerian‐like) mesh, whereas the structure (taken as a perfect conductor) is modelled with a conventional Lagrangian approach. The compatibility between the potential of the conductor and of the electric domain is obtained by introducing a Lagrange multiplier function, defined on the boundary of the conductor. The electromechanical forces are obtained using a variational formulation for the coupled electromechanical domain. We use a Heaviside function on the level set to remove the electric energy in the conductor domain. Results are presented for an radio frequency switch and an element of a comb drive. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

20.
    
A new method for the simulation of particulate flows, based on the extended finite element method (X‐FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

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