Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Chaudhry, Jehanzeb"'
Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The Poisson-Boltzmann equation
Externí odkaz:
http://arxiv.org/abs/2410.12810
Autor:
Chaudhry, Jehanzeb, Stevens, Zachary
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical MLMC algor
Externí odkaz:
http://arxiv.org/abs/2206.02905
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these bounds to the e
Externí odkaz:
http://arxiv.org/abs/2205.11580
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieves a threshold value on a given time interval. This quantity of interes
Externí odkaz:
http://arxiv.org/abs/2111.09834
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of "local" pro
Externí odkaz:
http://arxiv.org/abs/2111.00606
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of
Externí odkaz:
http://arxiv.org/abs/2009.11696
We present a reduced basis (RB) method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable error estimate is developed, and is shown to bound the error with respe
Externí odkaz:
http://arxiv.org/abs/2003.04555
Autor:
Chaudhry, Jehanzeb H., Collins, J. B.
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order approximation. In this
Externí odkaz:
http://arxiv.org/abs/2003.03399
Classical a posteriori error analysis for differential equations quantifies the error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the solution. In this work we consider a posteriori error estimates of a quan
Externí odkaz:
http://arxiv.org/abs/2001.11139
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive overlapping Schwarz
Externí odkaz:
http://arxiv.org/abs/1907.01139