Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation.

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties.

Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes.

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.

A fast boundary element method for the scattering analysis of high-intensity focused ultrasound.

High-intensity focused ultrasound (HIFU) techniques are promising modalities for the non-invasive treatment of cancer. For HIFU therapies of, e.g.

Correcting electrode modelling errors in EIT on realistic 3D head models.

Electrical impedance tomography (EIT) is a promising medical imaging technique which could aid differentiation of haemorrhagic from ischaemic stroke in an ambulance. One challenge in EIT is the ill-posed nature of the image reconstruction, i.e.

A fast parallel solver for the forward problem in electrical impedance tomography.

Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and the resulting surface voltages are measured. It has the potential to distinguish between ischaemic and haemorrhagic stroke with a portable and inexpensive device. The image reconstruction relies on an accurate forward model of the experimental setup.

Stroke type differentiation using spectrally constrained multifrequency EIT: evaluation of feasibility in a realistic head model.

We investigate the application of multifrequency electrical impedance tomography (MFEIT) to imaging the brain in stroke patients. The use of MFEIT could enable early diagnosis and thrombolysis of ischaemic stroke, and therefore improve the outcome of treatment. Recent advances in the imaging methodology suggest that the use of spectral constraints could allow for the reconstruction of a one-shot image.

Quantum mushroom billiards.

We report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. A. Bunimovich [Chaos 11, 802 (2001)].