A wave-based numerical scheme for damage detection and identification in two-dimensional composite structures

Previous studies on wave inspection in different propagation directions have focussed on the analysis of wave propagation and wave scattering from various types of joints in two-dimensional monolayered structures. In this work, a Finite Element (FE) based numerical scheme is presented for quantifying wave interaction with localised structural damage within two-dimensional layered composite structures having arbitrary layering, complexities and material characteristics. The scheme discretise a damaged structural medium into a system of N healthy substructures (waveguides) connected through a joint which bears the localised structural damage/discontinuity. Wave propagation constants along different propagation directions of the substructures are sought by combining Periodic Structure Theory (PST) and the FE method. The damaged joint is modelled using standard FE approach, ensuring joint-substructures mesh conformity. This is coupled to the obtained wave propagation constants in order to determine scattering coefficients for the wave interaction with damage in different propagation directions within the structure. Wave interaction coefficients for different damage types and structural parameters are analysed in order to establish an optimum basis for detecting and identifying damage, as well as assessing the orientation and extent of the detected damage. The main advantage of this scheme is precise predictions at a very low computational cost

A symmetry-adapted numerical scheme for SDEs

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the symmetry properties of the equation is introduced. Our algorithmic procedure is applied to the family of general linear SDEs for which two theoretical estimates of the numerical forward error are established.Comment: A numerical example adde

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap