456 citations · 639 across the 19 of their papers we have counts for
12 papers · 1 filter
Slip Wall Boundary Conditions in Curved Domains for Finite Element ALE Hydrodynamics
Nabil Atallah, Kevin Sweet, Paul Moujaes +3
We present a high-order finite element arbitrary Lagrangian-Eulerian (ALE) method for hydrodynamics with slip-wall boundary conditions on analytically curved domains. The method co…
High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity
Ketan Mittal, Veselin Dobrev, Tzanio Kolev +1
High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, b…
PDE-Constrained High-Order Mesh Optimization
Tzanio Kolev, Boyan Lazarov, Ketan Mittal +2
We present a novel framework for PDE-constrained -adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective fun…
A High-Order Shifted Interface Method for Lagrangian Shock Hydrodynamics
Nabil M. Atallah, Ketan Mittal, Guglielmo Scovazzi +1
We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on…
Weak Boundary Conditions for Lagrangian Shock Hydrodynamics: A High-Order Finite Element Implementation on Curved Boundaries
Nabil M. Atallah, Vladimir Z. Tomov, Guglielmo Scovazzi
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations…
Adaptive Surface Fitting and Tangential Relaxation for High-Order Mesh Optimization
Patrick Knupp, Tzanio Kolev, Ketan Mittal +1
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation a…
hr-adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm
Veselin Dobrev, Patrick Knupp, Tzanio Kolev +2
We present an -adaptivity framework for optimization of high-order meshes. This work extends the -adaptivity method for mesh optimization by Dobrev et al., where we utilized…
Simulation-Driven Optimization of High-Order Meshes in ALE Hydrodynamics
Veselin Dobrev, Patrick Knupp, Tzanio Kolev +3
In this paper we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible sho…
DSA Preconditioning for DG discretizations of transport and High-Order curved meshes
T. S. Haut, B. S. Southworth, P. G. Maginot +1
This paper derives and analyzes new diffusion synthetic acceleration (DSA) preconditioners for the SN transport equation when discretized with a high-order (HO) discontinuous Galer…
An Efficient Sweep-based Solver for the Equations on High-Order Meshes
T. S. Haut, P. G. Maginot, V. Z. Tomov +3
We propose a graph-based sweep algorithm for solving the steady state, mono-energetic discrete ordinates on meshes of high-order curved mesh elements. Our spatial discretization co…
The Target-Matrix Optimization Paradigm for High-Order Meshes
Veselin Dobrev, Patrick Knupp, Tzanio Kolev +2
We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of Knupp…
Algebraic Hybridization and Static Condensation with Application to Scalable H(div) Preconditioning
Veselin A. Dobrev, Tzanio V. Kolev, Chak S. Lee +2
We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by…