The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform

Anirudh Pradhan - One of the best experts on this subject based on the ideXlab platform.

Dan Jiao - One of the best experts on this subject based on the ideXlab platform.

  • a Deterministic Solution based fast eigenvalue solver with guaranteed convergence for finite element based 3 d electromagnetic analysis
    IEEE Transactions on Antennas and Propagation, 2013
    Co-Authors: Feng Sheng, Dan Jiao
    Abstract:

    A fast Solution to both the quadratic eigenvalue problem and the generalized eigenvalue problem is developed for the finite-element based analysis of general 3-D electromagnetic problems. Given an arbitrary frequency band of interest, denoting the number of physically important eigenvalues for this band by , the proposed eigenvalue Solution is capable of solving a significantly reduced eigenvalue problem of O(k) to find a complete set of eigenvalues and eigenvectors that are physically important for the given frequency band. In addition to bypassing the need of solving a large-scale eigenvalue problem of O(N), with N being the system matrix size, the reduced eigenvalue problem is constructed from O(k) Solutions to a Deterministic problem. As a result, the methods that have been developed to solve Deterministic problems and their fast solvers can all be readily leveraged to solve eigenvalue problems. Moreover, the proposed fast eigenvalue Solution has guaranteed convergence and controlled accuracy, which is theoretically proved in this paper. The Solution is applicable to general 3-D problems where the structures are arbitrary, materials are inhomogeneous, and both dielectrics and conductors can be lossy. Applications to microwave devices, package structures, and on-chip integrated circuits have demonstrated the accuracy, efficiency, and convergence of the proposed fast eigenvalue Solution.

  • a Deterministic Solution based fast quadratic eigenvalue solver for 3 d finite element analysis
    International Symposium on Antennas and Propagation, 2012
    Co-Authors: Feng Sheng, Dan Jiao
    Abstract:

    A fast Solution to the quadratic eigenvalue problem resulting from the finite element based analysis of general electromagnetic problems with lossy conductors and materials is developed. Given an arbitrary frequency band, the proposed solver is capable of solving a significantly reduced eigenvalue problem of O(k) to find a complete set of the eigenvalues and eigenvectors that are physically important for this frequency band, the number of which is k. The reduced eigenvalue problem is constructed from O(k) Solutions to a Deterministic problem. Its convergence and accuracy are theoretically proved. The proposed solver is applicable to general 3-D problems where the structures are arbitrary, materials are inhomogeneous, and both dielectrics and conductors can be lossy.

Anil Kumar Yadav - One of the best experts on this subject based on the ideXlab platform.

Barkha R. Tripathi - One of the best experts on this subject based on the ideXlab platform.

Alexander Alekseenko - One of the best experts on this subject based on the ideXlab platform.

  • Deterministic Solution of the spatially homogeneous boltzmann equation using discontinuous galerkin discretizations in the velocity space
    Journal of Computational Physics, 2014
    Co-Authors: Alexander Alekseenko, E Josyula
    Abstract:

    Abstract We present a new Deterministic approach for the Solution of the spatially homogeneous Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in the velocity space. In the new approach the collision operator has the form of a bilinear operator with a pre-computed kernel; its evaluation requires O ( n 5 ) operations at every point of the phase space where n is the number of degrees of freedom in one velocity dimension. The method is generalized to any molecular potential. Results of numerical simulations are presented for the problem of spatially homogeneous relaxation for the hard spheres potential. Comparison with the method of Direct Simulation Monte Carlo showed excellent agreement.

  • Deterministic Solution of the boltzmann equation using a discontinuous galerkin velocity discretization
    28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012, 2012
    Co-Authors: Alexander Alekseenko, E Josyula
    Abstract:

    We propose an approach for high order discretization of the Boltzmann equation in the velocity space using discontinuous Galerkin methods. Our approach employs a reformulation of the collision integral in the form of a bilinear operator with a time-independent kernel. In the fully non-linear case the complexity of the method is O(n8) operations per spatial cell where n is the number of degrees of freedom in one velocity direction. The new method is suitable for parallelization to a large number of processors. Techniques of automatic perturbation decomposition and linearisation are developed to achieve additional performance improvement. The number of operations per spatial cell in the linearised regime is O(n6). The method is applied to the Solution of the spatially homogeneous relaxation problem. Mass momentum and energy is conserved to a good precision in the computed Solutions.