4,497 research outputs found

    Modified Tangential Frequency Filtering Decomposition and its Fourier Analysis

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    In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter are determined by Fourier analysis. With this choice of the optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is O(h−23){\cal O}(h^{-\frac{2}{3}}), and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner

    Two sides tangential filtering decomposition

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    AbstractIn this paper we study a class of preconditioners that satisfy the so-called left and/or right filtering conditions. For practical applications, we use a multiplicative combination of filtering based preconditioners with the classical ILU(0) preconditioner, which is known to be efficient. Although the left filtering condition has a more sound theoretical motivation than the right one, extensive tests on convection–diffusion equations with heterogeneous and anisotropic diffusion tensors reveal that satisfying left or right filtering conditions lead to comparable results. On the filtering vector, these numerical tests reveal that e=[1,…,1]T is a reasonable choice, which is effective and can avoid the preprocessing needed in other methods to build the filtering vector. Numerical tests show that the composite preconditioners are rather robust and efficient for these problems with strongly varying coefficients

    Accurate computation of surface stresses and forces with immersed boundary methods

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    Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid-structure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a post-processing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems

    Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

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    Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

    Linear friction weld process monitoring of fixture cassette deformations using empirical mode decomposition

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    Due to its inherent advantages, linear friction welding is a solid-state joining process of increasing importance to the aerospace, automotive, medical and power generation equipment industries. Tangential oscillations and forge stroke during the burn-off phase of the joining process introduce essential dynamic forces, which can also be detrimental to the welding process. Since burn-off is a critical phase in the manufacturing stage, process monitoring is fundamental for quality and stability control purposes. This study aims to improve workholding stability through the analysis of fixture cassette deformations. Methods and procedures for process monitoring are developed and implemented in a fail-or-pass assessment system for fixture cassette deformations during the burn-off phase. Additionally, the de-noised signals are compared to results from previous production runs. The observed deformations as a consequence of the forces acting on the fixture cassette are measured directly during the welding process. Data on the linear friction-welding machine are acquired and de-noised using empirical mode decomposition, before the burn-off phase is extracted. This approach enables a direct, objective comparison of the signal features with trends from previous successful welds. The capacity of the whole process monitoring system is validated and demonstrated through the analysis of a large number of signals obtained from welding experiments

    A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

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    We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation.Comment: 33 pages, 9 figure

    Linear friction weld process monitoring of fixture cassette deformations using empirical mode decomposition

    Get PDF
    Due to its inherent advantages, linear friction welding is a solid-state joining process of increasing importance to the aerospace, automotive, medical and power generation equipment industries. Tangential oscillations and forge stroke during the burn-off phase of the joining process introduce essential dynamic forces, which can also be detrimental to the welding process. Since burn-off is a critical phase in the manufacturing stage, process monitoring is fundamental for quality and stability control purposes. This study aims to improve workholding stability through the analysis of fixture cassette deformations. Methods and procedures for process monitoring are developed and implemented in a fail-or-pass assessment system for fixture cassette deformations during the burn-off phase. Additionally, the de-noised signals are compared to results from previous production runs. The observed deformations as a consequence of the forces acting on the fixture cassette are measured directly during the welding process. Data on the linear friction-welding machine are acquired and de-noised using empirical mode decomposition, before the burn-off phase is extracted. This approach enables a direct, objective comparison of the signal features with trends from previous successful welds. The capacity of the whole process monitoring system is validated and demonstrated through the analysis of a large number of signals obtained from welding experiments
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