We investigate the ultra weak variational formulation for simulating time-harmonic Maxwell problems. This study has two main goals. First, we introduce a novel derivation of the UWVF method which shows that the UWVF is an unusual version of the standard upwind discontinuous Galerkin (DG) method with a special choice of basis functions. Second, we discuss the practical implementation of an electromagnetic UWVF solver. In particular, we propose a method to avoid the conditioning problems that are known to hamper the use of the UWVF for problems in general geometries and inhomogeneous media. In addition, we show how to implement the PML in the UWVF to accurately approximate physically unbounded problems and discuss the parallelization of the UWVF. Three dimensional numerical simulations are used to examine the feasibility of the UWVF for simulating wave propagation in inhomogeneous media and scattering from complex structures.

In this paper, a method for the determination of spatially varying thermal conductivity and perfusion coefficients of tissue is proposed. The temperature evolution in tissue is modelled with the Pennes bioheat equation. The main motivation here is a model-based optimal control for ultrasound surgery, in which the tissue properties are needed when the treatment is planned. The overview of the method is as follows. The same ultrasound transducers, which are eventually used for the treatment, are used to inflict small temperature changes in tissue. This temperature evolution is monitored using MR thermal imaging, and the tissue properties are then estimated on the basis of these measurements. Furthermore, an approach to choose transducer excitations for the determination procedure is also considered. The purpose of this paper is to introduce a method and therefore simulations are used to verify the method. Furthermore, computations are accomplished in a 2D spatial domain.

In this paper, interconversion between linear viscoelastic material functions is studied emphasizing materials with relatively fast rate of relaxation. The aim of this paper is to study the whole material function determination process from a linear viscoelastic experiment to interconversion by taking into account non-ideal loading and noisiness of the data in such an experiment. No assumptions are made concerning the form of the relaxation modulus or the creep compliance. Interconversion is carried out by evaluating numerically the convolution integral. Three different yet similar approaches are studied. In numerical interconversion, the resulting matrix equation is ill-posed. Due to this, Tikhonov regularization is applied to solve the related matrix system. Numerical simulations indicate that reliable results can be obtained with proposed numerical procedures.

One of the problems in ultrasound surgery is the long treatment times when large tumour volumes are sonicated. Large tumours are usually treated by scanning the tumour volume using a sequence of individual focus points. During the scanning, it is possible that surrounding healthy tissue suffers from undesired temperature rise. The selection of the scanning path so that the tumour volume is treated as fast as possible while temperature rise in healthy tissue is minimized would increase the efficiency of ultrasound surgery. The main purpose of this paper is to develop a computationally efficient method which optimizes the scanning path. The optimization algorithm is based on the minimum time formulation of the optimal control theory. The developed algorithm uses quadratic cost criteria to obtain the desired thermal dose in the tumour region. The derived method is evaluated with numerical simulations in 3D which are applied to ultrasound surgery of the breast in simplified geometry. Results from the simulations show that the treatment time as well as the total applied energy can be decreased from 16% to 43% as compared to standard sonication. The robustness of the optimized scanning path is studied by varying the perfusion and absorption in the tumour region.

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