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  • Open Access


    Reconstructing the Time-Dependent Thermal Coefficient in 2D Free Boundary Problems

    M. J. Huntul*

    CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 3681-3699, 2021, DOI:10.32604/cmc.2021.016036

    Abstract The inverse problem of reconstructing the time-dependent thermal conductivity and free boundary coefficients along with the temperature in a two-dimensional parabolic equation with initial and boundary conditions and additional measurements is, for the first time, numerically investigated. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For instance, steel annealing, vacuum-arc welding, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation of wells. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the… More >

  • Open Access


    Meshless method for solving a free boundary problem associated with obstacle

    DaMing Yuan, XiaoLiang Cheng

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.2, pp. 53-54, 2011, DOI:10.3970/icces.2011.017.053

    Abstract In this paper, we discuss the numerical method for solving the i??rst kind of elliptic variational inequality. We i??rst use the fundamental solution as the basis function to approximate the solution of variational inequality, then we employ the Uzawa's algorithm to determine the free boundary and the solution. Numerical examples are given to testify the efi??ciency of the method. More >

  • Open Access


    A comparison of the RBF-based meshfree boundary knot and the boundary particle methods

    W. Chen1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 177-188, 2007, DOI:10.3970/icces.2007.003.177

    Abstract This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of the singular fundamental solution to circumvent the controversial artificial boundary outside the physical domain. Compared with the boundary element method, both BKM and BPM are meshfree, super-convergent, integration-free, symmetric, and mathematically simple collocation techniques for general PDEs. In particular, the BPM does not… More >

  • Open Access


    Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method

    S.Y. Wang1,2, M.Y. Wang3

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119

    Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric RBF splines. To perform both… More >

  • Open Access


    Boundary Element Method for an Inverse Problem in Magnetic Resonance Imaging Gradient Coils

    Liviu Marin1, Henry Power1, Richard W. Bowtell2, Clemente Cobos Sanchez2, Adib A. Becker1, Paul Glover2,Arthur Jones1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 149-174, 2008, DOI:10.3970/cmes.2008.023.149

    Abstract We investigate the reconstruction of a divergence-free surface current distribution from knowledge of the magnetic flux density in a prescribed region of interest in the framework of static electromagnetism. This inverse problem is motivated by the design of gradient coils for use in magnetic resonance imaging (MRI) and is formulated using its corresponding integral representation according to potential theory. A novel boundary element method (BEM) which employs linear interpolation on quadratic surfaces and also satisfies the continuity equation for the current density, i.e. a divergence-free BEM, is presented. Since the discretised BEM system is ill-posed and hence the associated least-squares… More >

  • Open Access


    The Method of Fundamental Solutions for Eigenfrequencies of Plate Vibrations

    D.L. Young1,2, C.C. Tsai3, Y.C. Lin1, C.S. Chen4

    CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 1-10, 2006, DOI:10.3970/cmc.2006.004.001

    Abstract This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct determinant search method. Consequently analytical… More >

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