Mostak Ahmed

A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections

We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let

Finite horizon H∞ control for stochastic systems with multiple decision makers

G_{\rm c}

H ∞ constraint incentive Stackelberg game for discrete-time stochastic systems

denote the number of points per wavelength at the coarse level. If the coarse scale solutions are to approximate the true solutions, then the oscillatory nature of the solutions implies the requirement

H∞ Constraint Pareto Optimal Strategy for Stochastic LPV Systems

G_{\rm c} > 2

Group differential game approach of H2/H∞ control for large-scale linear stochastic systems

. However, in examples the requirement is more like

The Fatty Acid Composition and Properties of Oil Extracted from Fresh Rhizomes of Turmeric ( Curcuma longa Linn.) Cultivars of Bangladesh

G_{\rm c} \gtrsim 10

H∞-Constrained Incentive Stackelberg Game for Discrete-Time Systems with Multiple Non-cooperative Followers

, in a trade-off involving also the amount of damping present and the number of multigrid iterations. We conjecture that this is caused by the difference in phase speeds between the coarse and fine scale operators. Standard 5-point finite differences in two dimensions are our first example. A new coarse scale 9-point operator is constructed to match the fine scale phase speeds. We then compare phase speeds and multigrid performance of standard schemes with a scheme using the new operator. The required

A Note on Numerical Solution of a Linear Black-Scholes Model

G_{\rm c}

H ∞ -constrained incentive Stackelberg games for discrete-time stochastic systems with multiple followers

is reduced from about 10 to about 3.5, with less dam...

Multigrid for the Helmholtz equation: choice of the coarse scale operator

This paper investigates the finite horizon H∞ control problem for a class of nonlinear stochastic systems with multiple decision makers. First, it is shown that the H∞ controllers for the decision makers can be obtained by solving a dynamic Nash game problem. In order to find the H∞ controllers, necessary conditions for the existence of Nash equilibrium in the worst case disturbance, which consist of cross-coupled forward-backward stochastic differential equations (CFBSDEs), are derived by using stochastic maximum principle. Second, a four step scheme is adopted to develop a computational algorithm to solve the CFBSDEs. A simple practical example is solved to show the validity of the proposed method.