Inverse properties of a class of seven-diagonal (near) Toeplitz matrices

This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method

Applications and accuracy of the parallel diagonal dominant algorithm

The Parallel Diagonal Dominant (PDD) algorithm is a highly efficient, ideally scalable tridiagonal solver. In this paper, a detailed study of the PDD algorithm is given. First the PDD algorithm is introduced. Then the algorithm is extended to solve periodic tridiagonal systems. A variant, the reduced PDD algorithm, is also proposed. Accuracy analysis is provided for a class of tridiagonal systems, the symmetric, and anti-symmetric Toeplitz tridiagonal systems. Implementation results show that the analysis gives a good bound on the relative error, and the algorithm is a good candidate for the emerging massively parallel machines

Studies of magnetised and non-local transport in laser-plasma interactions

The application of magnetic fields in inertial fusion experiments has led to renewed interest in fully understanding magnetised transport in laser-plasma regimes. This motivated the development of a new laser magnetohydrodynamic code PARAMAGNET, written to support investigations into classical magnetised transport phenomena and laser propagation in a plasma. This code was used to simulate laser-underdense plasma interactions such as the pre-heat stage of magneto-inertial fusion. Alongside these simulations, this thesis will present analytic focusing and filamentation models derived from magnetohydrodynamics extended with classical magnetised transport coefficients. These results showed the focal length and filamentation growth length shortened with magnetisation, a result of the magnetisation of the thermal conductivity. Further investigation of the transport properties using the diffusion approximation kinetic code IMPACT showed significant deviation of the growth rate at intermediate values of magnetisation and non-locality, inexplicable using fluid models. The kinetic code result motivated exploring the influence of the high-order anisotropies of the distribution function (in terms of spherical harmonics), ignored in conventional approximations. By using a recursive matrix inverse method, corrections to the transport coefficients including all orders of the electron distribution expansion were found. Analysis of the conductivity, resistivity and thermoelectric coefficients showed deviation by up to 50% from the classical form at intermediate magnetisation and nonlocality. The diffusive approximation of the IMPACT simulations was insufficient to capture the transport behaviour present in the theoretical high order calculation. Modern inertial fusion experiments work in regimes that are non-local and susceptible to significant focusing exacerbated by magnetisation. The resulting filamentation has detrimental implications to laser absorption and the modified non-local transport behaviour is a possible source of error in simulations. The complex interplay between non-locality and magnetisation in transport suggests using more terms of the spherical harmonic expansion in closures of plasma equations. Particular consideration is given to the implications to inertial fusion experiments. Together these results suggest the necessity of including non-local magnetised transport in the modelling of high-energy-density laser plasma experiments.Open Acces

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks