Finite element methods for the simulation of wave propagation in soft viscoelastic biotissue

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Undertake research into finite element methods for the simulation of wave propagation in soft viscoelastic biotissue. The material will be modelled using Voigt and Maxwell type constitutive laws, the spatial discretization may be a continuous or discontinuous Galerkin or spectral finite element method, and the time discretization may be a classical finite difference scheme or a discontinuous or continuous finite element method. The research involves applied mathematics, numerical analysis, biomechanics and scientific computing, and its main aims are: 1. To design and mesh a family of human chest configurations, incorporating muscle, lung, bone, skin, fat, and a moving heart, for the purpose of modelling and simulating shear wave propagation from the areas associated with the coronary arteries to the chest surface. 2. To implement various numerical schemes, drawn from the techniques above, to determine the most suitable methods in terms of the accuracy and speed trade-off. This software will use existing open source resources and bespoke coding as necessary. This work is part of an ongoing multi-site and interdisciplinary project investigating the feasibility of non-invasive diagnosis of coronary artery disease using computational mathematics.