Aaron Fisher

A generalized mass lumping technique for vector finite-element solutions of the time-dependent Maxwell equations

Time-domain finite-element solutions of Maxwells equations require the solution of a sparse linear system involving the mass matrix at every time step. This process represents the bulk of the computational effort in time-dependent simulations. As such, mass lumping techniques in which the mass matrix is reduced to a diagonal or block-diagonal matrix are very desirable. In this paper, we present a special set of high order 1-form (also known as curl-conforming) basis functions and reduced order integration rules that, together, allow for a dramatic reduction in the number of nonzero entries in a vector finite element mass matrix. The method is derived from the Nedelec curl-conforming polynomial spaces and is valid for arbitrary order hexahedral basis functions for finite-element solutions to the second-order wave equation for the electric (or magnetic) field intensity. We present a numerical eigenvalue convergence analysis of the method and quantify its accuracy and performance via a series of computational experiments.

ALE-AMR: A New 3D Multi-Physics Code for Modeling Laser/Target Effects

We have developed a new 3D multi-physics multi-material code, ALE- AMR, for modeling laser/target effects including debris/shrapnel generation. The code combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) to connect the continuum to microstructural regimes. The code is unique in its ability to model hot radiating plasmas and cold fragmenting solids. New numerical techniques were developed for many of the physics packages to work efficiency on a dynamically moving and adapting mesh. A flexible strength/failure framework allows for pluggable material models. Material history arrays are used to store persistent data required by the material models, for instance, the level of accumulated damage or the evolving yield stress in J2 plasticity models. We model ductile metals as well as brittle materials such as Si, Be, and B4C. We use interface reconstruction based on volume fractions of the material components within mixed zones and reconstruct interfaces as needed. This interface reconstruction model is also used for void coalescence and fragmentation. The AMR framework allows for hierarchical material modeling (HMM) with different material models at different levels of refinement. Laser rays are propagated through a virtual composite mesh consisting of the finest resolution representation of the modeled space. A new 2 nd order accurate diffusion solver has been implemented for the thermal conduction and radiation transport packages. The code is validated using laser and x-ray driven spall experiments in the US and France. We present an overview of the code and simulation results.

Advancements in predictive plasma formation modeling

We present highlights from plasma simulations performed in collaboration with Lawrence Livermore National Labs. This modeling is performed to advance the rate of learning about optimal EUV generation for laser produced plasmas and to provide insights where experimental results are not currently available. The goal is to identify key physical processes necessary for an accurate and predictive model capable of simulating a wide range of conditions. This modeling will help to drive source performance scaling in support of the EUV Lithography roadmap. The model simulates pre-pulse laser interaction with the tin droplet and follows the droplet expansion into the main pulse target zone. Next, the interaction of the expanded droplet with the main laser pulse is simulated. We demonstrate the predictive nature of the code and provide comparison with experimental results.

Interface reconstruction in two- and three-dimensional arbitrary Lagrangian-Eulerian adaptive mesh refinement simulations

Modeling of high power laser and ignition facilities requires new techniques because of the higher energies and higher operational costs. We report on the development and application of a new interface reconstruction algorithm for chamber modeling code that combines ALE (Arbitrary Lagrangian Eulerian) techniques with AMR (Adaptive Mesh Refinement). The code is used for the simulation of complex target elements in the National Ignition Facility (NIF) and other similar facilities. The interface reconstruction scheme is required to adequately describe the debris/shrapnel (including fragments or droplets) resulting from energized materials that could affect optics or diagnostic sensors. Traditional ICF modeling codes that choose to implement ALE + AMR techniques will also benefit from this new scheme. The ALE formulation requires material interfaces (including those of generated particles or droplets) to be tracked. We present the interface reconstruction scheme developed for NIFs ALE-AMR and discuss how it is affected by adaptive mesh refinement and the ALE mesh. Results of the code are shown for NIF and OMEGA target configurations.

Multi-Material ALE with AMR for Modeling Hot Plasmas and Cold Fragmenting Materials

We have developed a new 3D multi-physics multi-material code, ALE-AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) to connect the continuum to the microstructural regimes. The code is unique in its ability to model hot radiating plasmas and cold fragmenting solids. New numerical techniques were developed for many of the physics packages to work efficiently on a dynamically moving and adapting mesh. We use interface reconstruction based on volume fractions of the material components within mixed zones and reconstruct interfaces as needed. This interface reconstruction model is also used for void coalescence and fragmentation. A flexible strength/failure framework allows for pluggable material models, which may require material history arrays to determine the level of accumulated damage or the evolving yield stress in J2 plasticity models. For some applications laser rays are propagating through a virtual composite mesh consisting of the finest resolution representation of the modeled space. A new 2nd order accurate diffusion solver has been implemented for the thermal conduction and radiation transport packages. One application area is the modeling of laser/target effects including debris/shrapnel generation. Other application areas include warm dense matter, EUV lithography, and material wall interactions for fusion devices.

Hierarchical material models for fragmentation modeling in NIF-ALE-AMR

Fragmentation is a fundamental process that naturally spans micro to macroscopic scales. Recent advances in algorithms, computer simulations, and hardware enable us to connect the continuum to microstructural regimes in a real simulation through a heterogeneous multiscale mathematical model. We apply this model to the problem of predicting how targets in the NIF chamber dismantle, so that optics and diagnostics can be protected from damage. The mechanics of the initial material fracture depend on the microscopic grain structure. In order to effectively simulate the fragmentation, this process must be modeled at the subgrain level with computationally expensive crystal plasticity models. However, there are not enough computational resources to model the entire NIF target at this microscopic scale. In order to accomplish these calculations, a hierarchical material model (HMM) is being developed. The HMM will allow fine-scale modeling of the initial fragmentation using computationally expensive crystal plasticity, while the elements at the mesoscale can use polycrystal models, and the macroscopic elements use analytical flow stress models. The HMM framework is built upon an adaptive mesh refinement (AMR) capability. We present progress in implementing the HMM in the NIF-ALE-AMR code. Additionally, we present test simulations relevant to NIF targets.

Laser Ray Tracing in a Parallel Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement Hydrocode

ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray tracing in ALE-AMR. We present the basic concepts of laser ray tracing and our approach to eciently traverse the adaptive mesh hierarchy.

An AMR Capable Finite Element Diffusion Solver for ALE Hydrocodes

We present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.

Modeling Heat Conduction and Radiation Transport with the Diffusion Equation in NIF ALE-AMR

The ALE-AMR code developed for NIF is a multi-material hydro-code that models target assembly fragmentation in the aftermath of a shot. The combination of ALE (Arbitrary Lagrangian Eulerian) hydro with AMR (Adaptive Mesh Refinement) allows the code to model a wide range of physical conditions and spatial scales. The large range of temperatures encountered in the NIF target chamber can lead to significant fluxes of energy due to thermal conduction and radiative transport. These physical effects can be modeled approximately with the aid of the diffusion equation. We present a novel method for the solution of the diffusion equation on a composite mesh in order to capture these physical effects.