Domain decomposition methods constitute a fundamental strategy in numerical analysis, enabling the partitioning of large and complex computational problems into smaller, more manageable sub-problems.

Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...

We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...

Analysis and implementation of numerical methods for random processes: random number generators, Monte Carlo methods, Markov chains, stochastic differential equations, and applications. Recommended ...

We study numerical methods for the one-dimensional inverse problem of reflection seismology. An impulsive plane wave in pressure is applied to the surface of a piecewise smooth stratified elastic half ...

Our work in numerical and scientific computing involves the development, analysis and execution of computational algorithms to solve mathematical problems from science and engineering. Our faculty are ...

In the collocating volatility (CLV) model, the stochastic collocation technique is used as a convenient representation of the terminal distribution of the market option prices. A specific dynamic is ...

Studying the equations of General Relativity and beyond, both analytically and with state-of-the-art simulations. Novel numerical and mathematical approaches can shed light on the structure and ...

In this paper, an efficient approach for the computation of the fair value of a basket option as well as its Greeks is presented. Both European and American options are considered; the determination ...