This paper deals with the numerical solution of the Heston partial differential equation (PDE) that plays an important role in financial option pricing theory, Heston (1993). A feature of this time-dependent, twodimensional convection-diffusion-reaction equation is the presence of a mixed spatial-derivative term, which stems from the correlation between the two underlying stochastic processes f...

This paper considers the application of numerical techniques to modelling large 3D Extremely Low Frequency (ELF) electromagnetic problems in the time and frequency domains. The environment model consists of three material layers: air, sea and seabed. To represent a coastal region, the sea region is shallow with a variable depth and includes a sloping seabed. The electromagnetic source is a harm...

We address the problem of computing a low-rank estimate Y of the solution X of the Lyapunov equation AX + XA′ + Q = 0 without computing the matrix X itself. This problem has applications in both the reduced-order modeling and the control of large dimensional systems as well as in a hybrid algorithm for the rapid numerical solution of the Lyapunov equation via the alternating direction implicit ...

We study a spline wavelet alternative direction implicit (SW-ADI) algorithm for solving two-dimensional reaction diffusion equations. This algorithm is based on a collocation method for PDEs with a specially designed spline wavelet for the Sobolev space H 2(I ) on a closed interval I. By using the tensor product nature of adaptive wavelet meshes, we propose a SW-ADI method for two-dimensional p...

Large degree-of-freedom real-time adaptive optics (AO) control requires reconstruction algorithms that are computationally efficient and readily parallelized for hardware implementation. In particular, we find the wave-front reconstruction for the Hudgin and Fried geometry can be cast into a form of the well-known Sylvester equation using the Kronecker product properties of matrices. We derive ...

Selective laser melting is developing into a standard manufacturing technology with applications in various sectors. However, the process is still far from being at par with conventional processes such as welding and casting, the primary reason of which is the unreliability of the process. While various numerical modelling and experimental studies are being carried out to better understand and ...

This paper is concerned with the numerical solution of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the so called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a ...

The interaction of intense ultrashort laser pulses with a gas of argon atoms is numerically investigated. The investigation utilizes a model that solves both the time-dependent Schrödinger equation and the wave equation self-consistently. The time-dependent Schrödinger equation for single-active electron in the effective static potential and in the potential of electron-laser interaction is sol...

We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the input space is finitedimensional, thi...