1,953 research outputs found
Accurate and efficient algorithms for boundary element methods in electromagnetic scattering: a tribute to the work of F. Olyslager
Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry's boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from F. Olyslager's scientific endeavors are included in the survey
Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques
We describe a numerical method to compute Casimir forces in arbitrary
geometries, for arbitrary dielectric and metallic materials, with arbitrary
accuracy (given sufficient computational resources). Our approach, based on
well-established integration of the mean stress tensor evaluated via the
fluctuation-dissipation theorem, is designed to directly exploit fast methods
developed for classical computational electromagnetism, since it only involves
repeated evaluation of the Green's function for imaginary frequencies
(equivalently, real frequencies in imaginary time). We develop the approach by
systematically examining various formulations of Casimir forces from the
previous decades and evaluating them according to their suitability for
numerical computation. We illustrate our approach with a simple
finite-difference frequency-domain implementation, test it for known geometries
such as a cylinder and a plate, and apply it to new geometries. In particular,
we show that a piston-like geometry of two squares sliding between metal walls,
in both two and three dimensions with both perfect and realistic metallic
materials, exhibits a surprising non-monotonic ``lateral'' force from the
walls.Comment: Published in Physical Review A, vol. 76, page 032106 (2007
Accelerating the Performance of a Novel Meshless Method Based on Collocation With Radial Basis Functions By Employing a Graphical Processing Unit as a Parallel Coprocessor
In recent times, a variety of industries, applications and numerical methods including the meshless method have enjoyed a great deal of success by utilizing the graphical processing unit (GPU) as a parallel coprocessor. These benefits often include performance improvement over the previous implementations. Furthermore, applications running on graphics processors enjoy superior performance per dollar and performance per watt than implementations built exclusively on traditional central processing technologies. The GPU was originally designed for graphics acceleration but the modern GPU, known as the General Purpose Graphical Processing Unit (GPGPU) can be used for scientific and engineering calculations. The GPGPU consists of massively parallel array of integer and floating point processors. There are typically hundreds of processors per graphics card with dedicated high-speed memory. This work describes an application written by the author, titled GaussianRBF to show the implementation and results of a novel meshless method that in-cooperates the collocation of the Gaussian radial basis function by utilizing the GPU as a parallel co-processor. Key phases of the proposed meshless method have been executed on the GPU using the NVIDIA CUDA software development kit. Especially, the matrix fill and solution phases have been carried out on the GPU, along with some post processing. This approach resulted in a decreased processing time compared to similar algorithm implemented on the CPU while maintaining the same accuracy
Numerical methods for computing Casimir interactions
We review several different approaches for computing Casimir forces and
related fluctuation-induced interactions between bodies of arbitrary shapes and
materials. The relationships between this problem and well known computational
techniques from classical electromagnetism are emphasized. We also review the
basic principles of standard computational methods, categorizing them according
to three criteria---choice of problem, basis, and solution technique---that can
be used to classify proposals for the Casimir problem as well. In this way,
mature classical methods can be exploited to model Casimir physics, with a few
important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture
Notes in Physics book on Casimir Physic
An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method
In this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in or external gradient-based optimization procedures. For speed, a model order reduction technique is used and the gradient computation is achieved by perturbation with geometry deformation, processed on the level of the individual mesh nodes. To maximize performance, the framework is targeted to multicore CPU architectures and its extended version can also use multiple GPUs. To illustrate the accuracy and high efficiency of the framework, we provide examples of simulations of a dielectric resonator antenna and full-wave design by optimization of two diplexers involving tens of unknowns, and show that the design can be completed within the duration of a few simulations using industry-standard FEM solvers. The accuracy of the design is confirmed by measurements
High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method
A new parallel solver for the volumetric integral equations (IE) of
electrodynamics is presented. The solver is based on the Galerkin method which
ensures the convergent numerical solution. The main features include: (i) the
memory usage is 8 times lower, compared to analogous IE based algorithms,
without additional restriction on the background media; (ii) accurate and
stable method to compute matrix coefficients corresponding to the IE; (iii)
high degree of parallelism. The solver's computational efficiency is shown on a
problem of magnetotelluric sounding of the high conductivity contrast media. A
good agreement with the results obtained with the second order finite element
method is demonstrated. Due to effective approach to parallelization and
distributed data storage the program exhibits perfect scalability on different
hardware platforms.Comment: The main results of this paper were presented at IAMG 2015 conference
Frieberg, Germany. 28 pages, 11 figure
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems
[EN] We consider the numerical solution of linear systems arising from computational electromagnetics applications. For large scale problems the solution is usually obtained iteratively with a Krylov subspace method. It is well known that for ill conditioned problems the convergence of these methods can be very slow or even it may be impossible to obtain a satisfactory solution. To improve the convergence a preconditioner can be used, but in some cases additional strategies are needed. In this work we study the application of spectral lowrank updates (SLRU) to a previously computed sparse approximate inverse preconditioner.The updates are based on the computation of a small subset of the eigenpairs closest to the origin. Thus, the performance of the SLRU technique depends on the method available to compute the eigenpairs of interest. The SLRU method was first used using the IRA s method implemented in ARPACK. In this work we investigate the use of a Jacobi Davidson method,
in particular its JDQR variant. The results of the numerical experiments show that the application of the JDQR method to obtain the spectral low-rank updates can be quite competitive compared with the IRA s method.Mas Marí, J.; Cerdán Soriano, JM.; Malla Martínez, N.; Marín Mateos-Aparicio, J. (2015). Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems. Journal of the Spanish Society of Applied Mathematics. 67:39-50. doi:10.1007/s40324-014-0025-6S395067Bergamaschi, L., Pini, G., Sartoretto, F.: Computational experience with sequential, and parallel, preconditioned Jacobi–Davidson for large sparse symmetric matrices. J. Comput. Phys. 188(1), 318–331 (2003)Carpentieri, B.: Sparse preconditioners for dense linear systems from electromagnetics applications. PhD thesis, Institut National Polytechnique de Toulouse, CERFACS (2002)Carpentieri, B., Duff, I.S., Giraud, L.: Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism. Numer. Linear Algebr. Appl. 7(7–8), 667–685 (2000)Carpentieri, B., Duff, I.S., Giraud, L.: A class of spectral two-level preconditioners. SIAM J. Sci. Comput. 25(2), 749–765 (2003)Carpentieri, B., Duff, I.S., Giraud, L., Magolu monga Made, M.: Sparse symmetric preconditioners for dense linear systems in electromagnetism. Numer. Linear Algebr. Appl. 11(8–9), 753–771 (2004)Carpentieri, B., Duff, I.S., Giraud, L., Sylvand, G.: Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations. SIAM J. Sci. Comput. 27(3), 774–792 (2005)Darve, E.: The fast multipole method I: error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38(1), 98–128 (2000)Fokkema, D.R., Sleijpen, G.L., Van der Vorst, H.A.: Jacobi–Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 20(1), 94–125 (1998)Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(3), 325–348 (1987)Grote, M., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Harrington, R.: Origin and development of the method of moments for field computation. IEEE Antenna Propag. Mag. (1990)Kunz, K.S., Luebbers, R.J.: The finite difference time domain method for electromagnetics. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Maxwell, J.C.: A dynamical theory of the electromagnetic field. Roy. S. Trans. CLV, (1864). Reprinted in Tricker, R. A. R. The Contributions of Faraday and Maxwell to Electrial Science, Pergamon Press (1966)Marín, J., Malla M.: Some experiments preconditioning via spectral low rank updates for electromagnetism applications. In: Proceedings of the international conference on preconditioning techniques for large sparse matrix problems in scientific and industrial applications (Preconditioning 2007), Toulouse (2007)Meijerink, J.A., van der Vorst, H.A.: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31, 148–162 (1977)Sorensen, D.C., Lehoucq, R.B., Yang, C.: ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM, Philadelphia (1998)Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antenna Propag. 30, 409–418 (1982)Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing Company, Boston (1996)Silvester, P.P., Ferrari, R.L.: Finite elements for electrical engineers. Cambridge University Press, Cambridge (1990)Sleijpen, S.L., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17, 401–425 (1996)van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 12(6), 631–644 (1992
Overview of Large-Scale Computing: The Past, the Present, and the Future
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