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HORSE

HORSE - High Order solver for Radar cross Section Evaluation

HORSE is a simulation software whose development has started in October 2014 in the context of the ANR TECSER project. HORSE is based on a high order HDG method formulated on unstructured tetrahedral and hybrid structured/unstructured (cubic/tetrahedral) meshes for solving the 3D system of frequency-domain Maxwell equations.

Characteristics of uniform tetrahdral meshes used for the numerical convergence study. Size of the discrete HDG systems for mesh M4.
HDG method for the three-dimensional frequency-domain Maxwell equations. Numerical convergence analysis considering the simple problem of a plane wave propagation in vacuum. A cubic domain is discretized using uniform tetrahedral meshes. Eh denotes the electric field, and Hh the magnetic field.
HDG-P1 method HDG-P2 method
HDG-P3 method HDG-P4 method

HDG method for the three-dimensional frequency-domain Maxwell equations. Plane wave propagation in vacuum. Strong scalability analysis: cluster with Intel Xeon Haswell E5-2680@2.5 GHz nodes, 24 cores per node, Infiniband QDR TrueScale 40Gb/s network. Solutions strategies for the hybrid variable system (globally coupled unknowns): MUMPS sparse direct solver, MaPHyS algebraic hybrid iterative-direct solver with MUMPS or PaStiX as a local sparse direct solver, GMRES accelerated Schwarz algorithm with PaStiX as a local sparse direct solver (referred as Krylov+BiCGStab6 in the figures).

HDG-P2 method HDG-P3 method

Scattering of a plane wave by the Lockheed F-104 Starfighter. Frequency of the incident wave: 600 MHz. Unstructured tetrahedral mesh with 1,645,874 elements and 3,521,251 faces.

Size of the discrete HDG systems
MaPHyS algebraic hybrid iterative-direct solver with PaStiX as a local sparse direct solver
Schwarz algorithm with PaStiX as a local sparse direct solver

Scattering of a plane wave by the Lockheed F-104 Starfighter. Frequency of the incident wave: 600 MHz. Strong scalability analysis: Occigen Bull/Atos cluster at CINES, Intel E5-2690, 2.6~GHz, 24 cores on each node, 64 GB or 128 GB RAM per node.