Guido Ala, Elisa Francomano, Antonino Spagnuolo

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Presentation transcript:

GRID Parallel Simulations of a Meshless Method for Electromagnetic Transients Guido Ala, Elisa Francomano, Antonino Spagnuolo Università degli Studi di Palermo Grid Open Days all’Università di Palermo Palermo, 6-7.12.2007

History SMOOTHED PARTICLE HYDRODYNAMICS (SPH) by Monaghan, Lucy, 1977 Used to solve Astrophysics and Fluid Dynamics problems Application to Electromagnetics (SPEM) Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Basic Ideas Domain discretization Arbitrary particle distribution Problem domain No connectivity law is needed (Meshfree) Particle representation Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Particle approximation of a function Basic Ideas Particle approximation of a function The value of the function in a particle is expressed by using the values of near particles, weighted by a suitable function W (Smoothing Kernel) Problem Domain Support domain Support Domains with the Smoothing Kernel Function Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

+ Formulation Integral representation of kernel approximation particle approximation Approximation of Number of particles in the support of the particle in x Smoothing length Problem Domain Smoothing kernel Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Dirac’s Function properties Smoothing Kernel Main properties Normalization Dirac’s Function properties Compactness Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Smoothing Kernel Gaussian Kernel B-Spline Kernel Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Smoothing Kernel By using the curl’s theorem If the support domain is fully into the problem domain The differential operator is directly applied to the kernel function Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Consistency If particles are irregularly distributed or there are domain zones with different distributions, the consistency condition for the kernel function may not be satisfied Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Variable distribution density of particles along the domain Consistency 1-D wave equations 0 < x < 1 t > 0 Variable distribution density of particles along the domain Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

With consistency restoration No consistency Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Consistency Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Consistency Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Maxwell’s curl Equations All EM phenomena can be described by mean of Maxwell’s curl equations and the constitutive relations of the media 1-D case Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Applications 2-D TM mode propagation in free space Simulation domain 80 x 80 cm2; 6400 particles PML Layers: 7 Source: Electric field Ez (gaussian pulse at timestep 1) Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Applications Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Field values calculation Applications CPU time (ms) Scalar 4 CPU parallel dW evaluation 19217 5730 Field values calculation 30 180 Data transferring - 40 Total time 19247 5950 Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

To do Optimal domain partitioning strategy 3-D model (in progress) Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Bibliography G.R. Liu, M.B. Liu “Smoothed Particle Hydrodynamics” World Scientific (2003) G.R. Liu, “Meshfree Methods”, CRC Press (2003) M. Lastiwka, N.Quinlan, M. Basa “Adaptive particle distribution for Smoothed Particle Hydrodynamics” Belytschko T., Krongauz Y., Dolbow J. and Gerlach C., “On the completeness of meshfree methods”, International Journal for Numerical Methods in Engineering, 43, pp. 785-819 (1998) Bonet J. and Lok T.-S. L., “Variational and momentum preservation aspects of Smooth Particle (1999) Hydrodynamics formulations”, Computer methods in applied mechanics and engineering, 180, pp. 97-115 Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007

Any Questions ? Thank you very much for your kind attention! Palermo, Grid Open Days all’Università di Palermo, 6-7.12.2007