153 citations · 547 across the 29 of their papers we have counts for
29 papers
An Anisotropic -Adaptation Framework for Ultraweak Discontinuous Petrov-Galerkin Formulations
Ankit Chakraborty, Stefan Henneking, Leszek Demkowicz
In this article, we present a three-dimensional anisotropic -mesh refinement strategy for ultraweak discontinuous Petrov--Galerkin (DPG) formulations with optimal test function…
Multistage DPG time-marching scheme for nonlinear problems
Judit Muñoz-Matute, Leszek Demkowicz
In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG met…
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
Jens Markus Melenk, Leszek Demkowicz, Stefan Henneking
In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the…
Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence
Jacob Badger, Stefan Henneking, Socratis Petrides +1
This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operat…
hp3D User Manual
Stefan Henneking, Leszek Demkowicz
User Manual for the hp3D Finite Element Software, available on GitHub at https://github.com/Oden-EAG/hp3d
Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions
Kamil Doległo, Anna Paszyńska, Maciej Paszyński +1
This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to app…
Stabilized finite element methods for a fully-implicit logarithmic reformulation of the Oldroyd-B constitutive law
Stefan Wittschieber, Leszek Demkowicz, Marek Behr
Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became p…
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
Yu Leng, Xiaochuan Tian, Leszek Demkowicz +2
We present a Petrov-Gelerkin (PG) method for a class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm…
An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics
Socratis Petrides, Leszek Demkowicz
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid t…
A numerical study of the pollution error and DPG adaptivity for long waveguide simulations
Stefan Henneking, Leszek Demkowicz
High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these probl…
Model and computational advancements to full vectorial Maxwell model for studying fiber amplifiers
Stefan Henneking, Jacob Grosek, Leszek Demkowicz
We present both modeling and computational advancements to a unique three-dimensional discontinuous Petrov-Galerkin finite element model for the simulation of laser amplification i…
A 3D DPG Maxwell Approach to Nonlinear Raman Gain in Fiber Laser Amplifiers
S. Nagaraj, J. Grosek, S. Petrides +2
We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach for modeling Raman gain in fiber laser amplifiers. In contrast with popular beam propagation models, w…
On perfectly matched layers for discontinuous Petrov-Galerkin methods
Ali Vaziri Astaneh, Brendan Keith, Leszek Demkowicz
In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, t…
Fast integration of DPG matrices based on tensorization
Jaime Mora, Leszek Demkowicz
Numerical integration of the stiffness matrix in higher order finite element (FE) methods is recognized as one of the heaviest computational tasks in a FE solver. The problem becom…
Goal-oriented adaptive mesh refinement for non-symmetric functional settings
Brendan Keith, Ali Vaziri Astaneh, Leszek Demkowicz
In this article, a new unified duality theory is developed for Petrov-Galerkin finite element methods. This novel theory is then used to motivate goal-oriented adaptive mesh refine…
DPG* Method
Brendan Keith, Leszek Demkowicz, Jay Gopalakrishnan
We introduce a cousin of the DPG method - the DPG* method - discuss their relationship and compare the two methods through numerical experiments.
High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations
Ali Vaziri Astaneh, Federico Fuentes, Jaime Mora +1
This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodo…
Discrete least-squares finite element methods
Brendan Keith, Socratis Petrides, Federico Fuentes +1
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator def…
Using a DPG method to validate DMA experimental calibration of viscoelastic materials
Federico Fuentes, Leszek Demkowicz, Aleta Wilder
A discontinuous Petrov-Galerkin (DPG) method is used to solve the time-harmonic equations of linear viscoelasticity. It is based on a "broken" primal variational formulation, which…
An ultraweak DPG method for viscoelastic fluids
Brendan Keith, Philipp Knechtges, Nathan V. Roberts +3
We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1,2]. In our…
A spacetime DPG method for the Schrodinger equation
Leszek Demkowicz, Jay Gopalakrishnan, Sriram Nagaraj +1
A spacetime Discontinuous Petrov Galerkin (DPG) method for the linear time-dependent Schrodinger equation is proposed. The spacetime approach is particularly attractive for capturi…
Coupled variational formulations of linear elasticity and the DPG methodology
Federico Fuentes, Brendan Keith, Leszek Demkowicz +1
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a dist…
The DPG methodology applied to different variational formulations of linear elasticity
Brendan Keith, Federico Fuentes, Leszek Demkowicz
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional…
Breaking spaces and forms for the DPG method and applications including Maxwell equations
C. Carstensen, L. Demkowicz, J. Gopalakrishnan
Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element i…