Showing papers by "Garth N. Wells published in 2020"
TL;DR: A new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem that has the attractive properties of full hybridized methods, namely an H({\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and error estimates for the velocity that are independent of the pressure.
44 citations
TL;DR: A strain transfer mechanism that also requires the rotation of the crystal lattice is demonstrated, which opens up new possibilities to improve the mechanical properties of polycrystals, as discussed.
Abstract: At the grain boundaries of plastically deforming polycrystals, strain transfer mechanisms can accommodate the shear strain carried by slip bands and mechanical twins to prevent stress build-ups and damage. So far, only the accommodation obtained through slip (and twinning) alone has been considered in the mechanism known as slip (and twin) transfer. Here, a strain transfer mechanism that also requires the rotation of the crystal lattice is demonstrated. A region of accumulated slip develops perpendicular to the active slip plane in the impinged grain. The slip gradients enable a localized lattice rotation that accommodates the shear strain in the incoming band, preventing the build-up of interfacial stresses. The mechanism operates preferentially at the boundaries between highly misoriented grains. Facilitating strain transfer at these interfaces opens up new possibilities to improve the mechanical properties of polycrystals, as discussed.
17 citations
TL;DR: An embedded-hybridized discontinuous Galerkin (EDG-HDG) method is introduced for the coupled Stokes-Darcy system, a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain.
13 citations
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TL;DR: This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to wavelength of the harmonic, and shows that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing.
Abstract: The numerical simulation of nonlinear ultrasound is important in the treatment planning for high-intensity focused ultrasound (HIFU) therapies in the abdomen. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus.
Numerical experiments are performed for HIFU transducers in homogeneous media in order to determine the size of the separate meshes required to accurately represent the harmonics. In particular, a fast volume potential (VP) approach is proposed and employed to perform convergence experiments as the computation domain size is modified. The VP approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing.
1 citations
TL;DR: In this article, the authors proposed a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic, and the increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size.
Abstract: The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus.
Numerical experiments are performed for FUS transducers in homogeneous media in order to determine the size of the meshes required to accurately represent the harmonics. In particular, a fast \emph{volume potential} approach is proposed and employed to perform convergence experiments as the computation domain size is modified. This approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing. Finally, it is demonstrated how to generalise this approach to inhomogeneous propagation domains.