Related papers: Multigrid Iterative Algorithm based on Compact Fin…

We present a reduced basis method for the simulation of American option pricing. To tackle this model numerically, we formulate the problem in terms of a time dependent variational inequality. Characteristic ingredients are a POD-greedy and…

This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…

When solving the American options with or without dividends, numerical methods often obtain lower convergence rates if further treatment is not implemented even using high-order schemes. In this article, we present a fast and explicit…

For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…

In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…

Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations…

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…

For pricing American options, %after suitable discretization in space and time, a sequence of discrete linear complementarity problems (LCPs) or equivalently Hamilton-Jacobi-Bellman (HJB) equations need to be solved in a sequential…

For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…

We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$…

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation…

This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL…

This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…

We investigate multi-stage demand uncertainty for the multi-item multi-echelon capacitated lot sizing problem with setup carry-over. Considering a multi-stage decision framework helps to quantify the benefits of being able to adapt…

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as \begin{equation*}…

We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the…

We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem, some forms of which are the vector M-Pad\'e approximation problem in [Van Barel and…

This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…

In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial…