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.

Circulant preconditioning in the volume integral equation method for silicon photonics.

Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation tool for silicon photonics applications [J. Lightw. Technol.