9 papers
Order Reduction of Exponential Runge--Kutta Methods: Fourth-Order Schemes for Non-Commuting Operators
Thi Tam Dang, Pablo Alexei Gazca-Orozco, Trung Hau Hoang
This paper extends the convergence analysis of explicit exponential Runge--Kutta methods for linear parabolic problems , where generates an analytic semi…
Well-posedness of nonlinear parabolic equations with unbounded drift via nonlinear evolution theory
Thi Tam Dang, Trung Hau Hoang, Giandomenico Orlandi +1
We develop a nonlinear evolution framework for nonlinear parabolic equations with unbounded drift terms formulated in Lorentz spaces. The main contribution lies in the construction…
From Memory Model to CPU Time: Exponential Integrators for Advection-Dominated Problems
Thi Tam Dang, Trung Hau Hoang
In this paper, we investigate the application of exponential integrators to advection-dominated problems. We focus on Krylov subspace and Leja interpolation methods to compute the…
Interior point methods for an algebraic system involving complementarity equations for geomechanical fractures
Trung Hau Hoang
Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary valu…
How to avoid order reduction in third-order exponential Runge--Kutta methods for problems with non-commutative operators?
Thi Tam Dang, Trung Hau Hoang
This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods…
Should exponential integrators be used for advection-dominated problems?
Lukas Einkemmer, Trung-Hau Hoang, Alexander Ostermann
In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context,…
Order Reduction of Exponential Runge--Kutta Methods: Non-Commuting Operators
Trung Hau Hoang
Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient nu…
Adapted Lie splitting method for convection-diffusion problems with singular convective term
Thi Tam Dang, Trung Hau Hoang, Giandomenico Orlandi
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to co…
Existence for noncoercive nonlinear elliptic equations with two lower-order terms
Thi Tam Dang, Trung Hau Hoang
This paper considers a class of noncoercive nonlinear elliptic problems with coefficients defined in Marcinkiewicz and Lorentz spaces. We prove the existence of a solution for the…