As fusion simulation codes increasingly account for the full geometric complexity of magnetically confined fusion systems, a need arose to provide tailored unstructured mesh technologies to address the specific needs of fusion plasma simulation codes and their coupling to other physics simulation codes. This paper presents a high level overview of a set of unstructured mesh developments that include; methods to effectively employ manufacturing CAD models in the construction of quality analysis model geometries, specialized mesh generation and adaptation tools; an infrastructure to support parallel particle-in-cell calculation on unstructured meshes; and an infrastructure for coupling of massively parallel mesh-based fusion codes.

Many engineering problems are characterized as having complex geometry that evolves over time combined with complex physical behaviors. In addition to an appropriate combination of physics models, discretization techniques and numerical methods, the effective simulation of such problems requires a set of methods to track the evolution of the simulation domain and the spatial decomposition of that domain into the desired meshes. This paper presents a set of geometry model representation and mesh generation/update procedures developed, and combined, to support the simulation of evolving geometry problems. The geometry representation and tracking procedures presented are designed to effectively interact with complex CAD representations while providing an effective means to account for sliding interfaces for which the base model topology changes. The mesh generation procedures combine automatic boundary layer and unstructured mesh generation with procedures to effectively generate semi-structured meshes in confined regions of geometry that can include step variations. The mesh update procedures combine mesh motion and local cavity mesh modification to provide well controlled, and adapted, meshes throughout an evolving geometry simulation.

Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell-matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

Realistic simulation of electromagnetic wave propagation in the actual human body can expedite the investigation of the phenomenon of harvesting implanted devices using wireless powering coupled from external sources. The parallel electromagnetics code suite ACE3P developed at SLAC National Accelerator Laboratory is based on the finite element method for high fidelity accelerator simulation, which can be enhanced to model electromagnetic wave propagation in the human body. Starting with a CAD model of a human phantom that is characterized by a number of tissues, a finite element mesh representing the complex geometries of the individual tissues is built for simulation. Employing an optimal power source with a specific pattern of field distribution, the propagation and focusing of electromagnetic waves in the phantom has been demonstrated. Substantial speedup of the simulation is achieved by using multiple compute cores on supercomputers.

This paper presents a parallel adaptive mesh control procedure designed to operate with high-order finite element analysis packages to enable large-scale automated simulations on massively parallel computers. The curved mesh adaptation procedure uses curved entity mesh modification operations that explicitly consider the influence of the curved mesh entities on element shape. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

Domain descriptions for numerical analyses originating from 3D images pose significant challenges as they have to be converted to a discretization suitable for a numerical analysis. Methods that perform this process by converting the image data directly to an analysis mesh suffer from a number of disadvantages with respect to both the flexibility to create well controlled meshes, and with respect to the ability to effectively represent the heterogeneous material regions of the imaged domain. We will present an alternative approach that avoids disadvantages through the construction of a non-manifold model representation.

This paper presents the development of a parallel adaptive mesh control procedure designed to operate with high-order finite element analysis packages to enable large scale automated simulations on massively parallel computers. The curved mesh adaptation procedure uses curved entity mesh modification operations. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

This chapter presents a set of procedures that start from image data to construct a non-manifold geometric model that supports the effective generation of meshes with the types of mesh configurations and gradations needed for efficient simulations. The types of operations needed to process the image information before and during the creation of the non-manifold geometric domains are outlined, with emphasis on those methods that are most appropriate for the analysis of materials system’s behavior.

The adaptive variable p- and hp-version finite element method can achieve exponential convergence rate when a near optimal finite element mesh is provided. For general 3D domains, near optimal p-version meshes require large curved elements over the smooth portions of the domain, geometrically graded curved elements to the singular edges and vertices, and a controlled layer of curved prismatic elements in the thin sections. This paper presents a procedure that accepts a CAD solid model as input and creates a curved mesh with the desired characteristics. One key component of the procedure is the automatic identification of thin sections of the model through a set of discrete medial surface points computed from an Octree-based tracing algorithm and the generation of prismatic elements in the thin directions in those sections. The second key component is the identification of geometric singular edges and the generation of geometrically graded meshes in the appropriate directions from the edges. Curved local mesh modification operations are applied to ensure the mesh can be curved to the geometry to the required level of geometric approximation.

AbstractBuilding on a general abstraction of the steps and transformations of a multiscale analysis, this chapter considers an approach to the development of multiscale simulation in which interoperable components can be effectively combined to address a wide range of multiscale simulations. Key concerns in the development of these interoperable components are maximizing the ability to use existing single simulation tools and supporting adaptive simulation control methods. In addition to indicating specific tools that have been developed to support multiscale simulations, an example adaptive atomistic/continuum simulation procedure is demonstrated.

As part of Rensselaer's ONR/ARPA URI on Mechanism-Based Modeling of Composite Structures a set of computational and visualization tools are being developed and integrated together to provide scientists and engineers with the means to better design composite materials and structures. This paper briefly overviews the modular software framework which underlies the system. Some of the underlying computational techniques critical to the numerical analysis procedures are introduced, such as adaptive multiscale modeling based on hierarchic superposition techniques and effective unit cell and other micromechanical models. This paper shows examples of the application of these techniques to understanding the behavior of composite materials and structures.

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

A software framework supporting mechanism-based design of high temperature composite structures is described. The framework extends material property databases by allowing the investigation and simulation of small scale behaviors which cause full scale effects. The framework integrates a full range of modeling processes, including automated model generation tools, numerically efficient analysis codes, post-processing and visualization, so as to minimize the effort required to develop mechanism-based models for new behaviors and materials.

This paper considers the technologies needed to support the creation of adaptively constructed meshes for general curved three-dimensional domains and outlines one set of solutions for providing them. A brief review of an effective way to integrate mesh generation/adaptation with CAD geometries is given. A set of procedures that support general h-adaptive refinement based on a mesh metric field is given. This is followed by examples that demonstrate the ability of the procedures to adaptively construct anisotropic meshes for flow problems. A procedure for the generation of strongly graded, curved meshes as needed for effective hp-adaptive simulations is also given.

This paper discusses a system for automated analysis of crack propagation in heterogeneous materials.The system uses a multiscale analysis technique to account for the effect of the microstructure on the propagation of the crack.The multiscale analysis allows the microstructure of the composite to be explicitly represented in the vicinity of the crack front while using homogenized material properties elsewhere.Procedures for automatic construction and update of the models and meshes used in the analysis are described.

One of the major issues of mesh generation today is access to geometry in an accurate and efficient manner. This paper will review several of the issues associated with accessing geometry for mesh generation. This paper will also evaluate alternative techniques for accessing geometry and review how these techniques address, or do not address, the issues related to geometry access for mesh generation. The techniques for geometry access to be reviewed include: translation and healing, discrete representations, direct geometry access, and unified topology accessing geometry directly. The intent of this paper is to provide an overview to the alternative approaches and how they address the specific issues related to accessing geometry for mesh generation. It is not the intent of this paper to provide detailed algorithms related to accessing or repairing geometry data.

This paper discusses the technologies needed to support the application of simulation-based design. Emphasis is placed on the technical components that must be added to existing CAD and CAE tools to enable the application of simulation-based design. These components include a simulation model manager, simulation data manager, adaptive control tools and simulation model generators. The application of these technologies to automotive climate control system design is demonstrated.

Although computer-aided engineering (CAE) technologies are a critical component to the engineering design process, their effective integration into design processes continues to be awkward. This has been particularly true of more advanced simulation technologies such as finite element analysis. Developments over the past decade on technologies like the automatic generation of finite element mesh, and other analysis discretizations, directly from solid model representations [1,8] provide one of the tools to allow the effective use of simulation during design. However, a number of additional capabilities and structures are needed to truly integrate the simulation technologies into engineering design.