Journal: Journal of Computational and Applied Mathematics

Abbreviation

J. Comput. Appl. Math.

Publisher

Elsevier

Journal Volumes

ISSN

0377-0427
0771-050X
1879-1778

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Publications1 - 10 of 23
  • Approximation order of interpolatory nonlinear subdivision schemes
    Item type: Conference Paper
    Dyn, Nira; Grohs, Philipp; Wallner, Johannes (2010)
    Journal of Computational and Applied Mathematics
  • Coupled boundary and volume integral equations for electromagnetic scattering
    Item type: Journal Article
    Labarca Figueroa, Ignacio; Hiptmair, Ralf (2025)
    Journal of Computational and Applied Mathematics
    We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle Ω⊂R3. From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on Ω. Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.
  • Implicit–explicit schemes for flow equations with stiff source terms
    Item type: Journal Article
    Svärd, Magnus; Mishra, Siddhartha (2011)
    Journal of Computational and Applied Mathematics
  • Optimality of adaptive Galerkin methods for random parabolic partial differential equations
    Item type: Journal Article
    Gittelson, Claude Jeffrey; Andreev, Roman; Schwab, Christoph (2014)
    Journal of Computational and Applied Mathematics
  • Fractional derivative for interpolation in Rn and SO(n) applications in functionally graded materials and rigid body transformations
    Item type: Journal Article
    Hua, Hao; Hovestadt, Ludger; Biao, Li (2020)
    Journal of Computational and Applied Mathematics
  • Bandlimited shearlet-type frames with nice duals
    Item type: Journal Article
    Grohs, Philipp (2013)
    Journal of Computational and Applied Mathematics
    The present paper constructs a frame/dual frame pair of shearlet type such that both frames possess the distinctive time–frequency localization properties needed in establishing their desirable approximation properties. Our construction is based on a careful pasting together of two bandlimited shearlet Parseval frames associated with two different frequency cones, inspired by domain decomposition methods used primarily for the solution of PDEs.
  • Fourth international conference on finite element methods in engineering and sciences (FEMTEC 2013)
    Item type: Other Conference Item
    Solin, Pavel; Karban, Pavel; Schnepp, Sascha (2014)
    Journal of Computational and Applied Mathematics
  • A low-complexity algorithm to digitally uncouple the mutual coupling effect in antenna arrays via symmetric Toeplitz matrices
    Item type: Journal Article
    Perera, Sirani M.; Lingsch, Levi; Madanayake, Arjuna; et al. (2026)
    Journal of Computational and Applied Mathematics
    In this paper, we solve systems of linear equations having an n×n coefficient matrix as a symmetric Toeplitz matrix having elements found via the measured mutual coupling effects of electromagnetic fields caused by antenna array elements. This coefficient matrix is called the mutual coupling matrix. In general, these mutual coupling matrices are characterized as dense matrices. However,building on our prior work, we have introduced a symmetric Toeplitz structure, defining its elements through the self- and mutual coupling effects of antenna array elements. Thus, in this paper, we propose an algorithm to uncouple the mutual coupling effect of antenna arrays using O(nlog(n)) as opposed to O(n3) complexity while defining the mutual coupling matrix as a matrix defined by the structure, i.e., a symmetric Toeplitz matrix. The proposed mutually coupled systems will be solved using a sparse factorization of the uncoupling matrices consisting of diagonal and butterfly matrices. The proposed algorithm has low arithmetic complexity compared to brute-force computations in solving systems of linear equations associated with mutual coupling matrices. The proposed factorization also leads to an alternative method to solve the system of linear equations having symmetric Toeplitz matrices as coefficient matrices with O(nlog(n)) as opposed to the O(n3) complexity algorithm. To evaluate the accuracy and efficiency of the proposed Toeplitz solver, we have benchmarked our algorithm against highly optimized libraries such as SciPy, NumPy, and PyTorch, specifically focusing on operations involving Toeplitz system solvers and inversion. We show that the proposed Toeplitz solver achieves exceptional efficiency, especially when utilizing GPU acceleration in PyTorch, all while maintaining accuracy. For the demonstration of numerical results based on the proposed digital uncoupling algorithm and the effect of attenuation, we use S-parameters at 1.4 GHz of an 8-element sub-array and a 16-element sub-array. We show that the diagonal elements of the uncoupling matrices steadily decrease as one moves away from the main diagonal, highlighting the diminishing effect of mutual coupling and the predominance of self-coupling over mutual coupling. Finally, an 8-element signal flow graph will be presented to show the uncoupling of mutual coupling effects of antenna arrays in digital signal processing perspective.
  • Discontinuous Galerkin methods with Trefftz approximations
    Item type: Conference Paper
    Kretzschmar, Fritz; Schnepp, Sascha M.; Tsukermann, Igor; et al. (2014)
    Journal of Computational and Applied Mathematics
  • A discrete model for force-based elasticity and plasticity
    Item type: Journal Article
    Dassios, Ioannis; Tzounas, Georgios; Milano, Federico; et al. (2024)
    Journal of Computational and Applied Mathematics
    The article presents a mathematical model that simulates the elastic and plastic behaviour of discrete systems representing isotropic materials. The systems consist of one lattice of nodes connected by edges and a second lattice with nodes placed at the centres of the existing edges. The derivation is based on the assumption that the kinematics of the second lattice is induced by the kinematics of the first, and uses stored energies in edges of both lattices to derive a edge forces in the first lattice. This leads to a non-linear system of algebraic equations describing elasticity and plasticity in lattices. A numerical solution to the non-linear system is proposed by providing a matrix formulation necessary for software implementation. An illustrative example is given to justify the formulation and demonstrate the system behaviour.
Publications1 - 10 of 23