Author

# Omar Laghrouche

Other affiliations: Durham University, École centrale de Nantes

Bio: Omar Laghrouche is an academic researcher from Heriot-Watt University. The author has contributed to research in topics: Finite element method & Track (rail transport). The author has an hindex of 23, co-authored 96 publications receiving 1757 citations. Previous affiliations of Omar Laghrouche include Durham University & École centrale de Nantes.

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##### Papers

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TL;DR: In this article, the effect of railway vibrations on passenger comfort and track performance is evaluated and the most suitable mathematical and numerical modelling strategies for railway vibration simulation, along with mitigation strategies are discussed.

187 citations

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TL;DR: In this article, a 3D finite element coupled train-track model for the numerical modelling of the ground induced vibration due to the passage of a single high speed train locomotive is investigated.

133 citations

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TL;DR: In this article, a finite element model for the solution of Helmholtz problems at higher frequencies is described, which offers the possibility of computing many wavelengths in a single finite element.

Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

131 citations

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TL;DR: In this article, the authors developed finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength.

Abstract: The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.

121 citations

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TL;DR: A new type of approximation for the potential is described in which the usual finite–element and boundary–element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere.

Abstract: Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.

107 citations

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631 citations

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01 Jan 1998TL;DR: In this article, the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7.

Abstract: The goal of this final chapter is to show how the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters. This will be done by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7. Additional applications are developed in the Exercises. The primary solution method is Fourier’s method of separation of variables and the associated Sturm-Liouville theory of Chapter 8.

530 citations

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TL;DR: A finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it is proposed, expected to attain high coarse-mesh accuracy without significant degradation of conditioning.

376 citations