ETHOS: Enabling Technologies for HighOrder Simulations
The Enabling Technologies for HighOrder Simulations (ETHOS) project performs research of fundamental mathematical technologies for nextgeneration highorder simulations algorithms. The current focus is on advancing the theoretical understanding and practical utility of unstructured meshes with arbitrarily highorder curvilinear elements by researching key challenges associated with highorder mesh quality optimization and simulationdriven adaptivity.
With support from the Applied Mathematics research program in the Department of Energy (DOE) Office of Science, the ETHOS team performs basic research that is broadly applicable to many highorder simulation approaches, including highorder finite elements and tightly coupled arbitrary LagrangianEulerian (ALE) simulations of interest to the DOE. Our research builds on the TargetMatrix Optimization Paradigm (TMOP) and nonlinear variational minimization to develop new nodemovement strategies for highorder mesh quality optimization and adaptation in both purely geometric settings, as well as in the context of a given physical simulation.
Project summary
Highorder meshes are difficult to control
 Highorder simulations rely on highorder meshes, and bad mesh quality leads to small time steps and applications failures.
 In addition to good geometric quality, applications can require highorder mesh adaptivity to dynamic simulation features.
Our solution: Develop theory that rigorously defines highorder mesh quality
 We are extending the TMOP of Knup to highorder meshes, defining pointwise quality based on subzonal information, and optimizing the mesh node positions with respect to an aggregated quality measure.
 We are exploring (nonlinear) solvers for the global optimization problem, incorporating research in constrained optimization, linear and nonlinear solvers, and preconditioners.
Impact: Mesh optimization is relevant to a wide range of applications
 Our research targets moving mesh applications (e.g., ALE methods) and applications where symmetry preservation or adaptation to physics is important (e.g., inertial confinement fusion [ICF] and tokamak magnetohydrodynamics).
 We are also interested in mesh generation, surface optimization, h and hprefinement, and more.
 The ETHOS algorithms are freely available on the MFEM website.
Team

Vladimir Tomov (LLNL)

Patrick Knupp (Dihedral, LLC)

Tzanio Kolev (LLNL) – Project Leader

Veselin Dobrev (LLNL)

Ketan Mittal (UIUC) – Summer Intern 2017, 2018
Software
 Many of the highorder mesh optimization algorithms developed in the ETHOS project are freely available in a userfriendly form in the MFEM finite element library.
 See in particular the Mesh Optimizer miniapp in the miniapps/meshing directory and the TMOP sources in the fem directory.
Publications
 V. Dobrev, P. Knupp, Tz. Kolev, and V. Tomov, Towards SimulationDriven Optimization of HighOrder Meshes by the TargetMatrix Optimization Paradigm, 27th International Meshing Roundtable technical paper, (2018).
 V. Dobrev, P. Knupp, Tz. Kolev, K. Mittal, and V. Tomov, The TargetMatrix Optimization Paradigm for HighOrder Meshes, SIAM J. Sci. Comput., 41(1), pp. B50–B68, (2019).
 R. Anderson, V. Dobrev, Tz. Kolev, R. Rieben, and V. Tomov, HighOrder MultiMaterial ALE Hydrodynamics, SIAM J. Sci. Comp., Vol. 40(1), pp. B32–B58, (2018).
 P. Knupp, Introducing the targetmatrix paradigm for mesh optimization by node movement, Engineering with Computers 28(4), pp. 419–429, (2012).