Xiaojuan Luo

Automatic p-version mesh generation for curved domains

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.

An Interoperable, Data-Structure-Neutral Component for Mesh Query and Manipulation

Much of the effort required to create a new simulation code goes into developing infrastructure for mesh data manipulation, adaptive refinement, design optimization, and so forth. This infrastructure is an obvious target for code reuse, except that implementations of these functionalities are typically tied to specific data structures. In this article, we describe a software component---an abstract data model and programming interface---designed to provide low-level mesh query and manipulation support for meshing and solution algorithms. The component’s data model provides a data abstraction, completely hiding all details of how mesh data is stored, while its interface defines how applications can interact with that data. Because the component has been carefully designed to be general purpose and efficient, it provides a practical platform for implementing high-level mesh operations independently of the underlying mesh data structures. After describing the data model and interface, we provide several usage examples, each of which has been used successfully with multiple implementations of the interface functionality. The overhead due to accessing mesh data through the interface rather than directly accessing the underlying mesh data is shown to be acceptably small.

Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method

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.

Moving curved mesh adaptation for higher-order finite element simulations

Higher-order finite element method requires valid curved meshes in three-dimensional domains to achieve the solution accuracy. When applying adaptive higher-order finite elements in large-scale simulations, complexities that arise include moving the curved mesh adaptation along with the critical domains to achieve computational efficiency. This paper presents a procedure that combines Bézier mesh curving and size-driven mesh adaptation technologies to address those requirements. A moving mesh size field drives a curved mesh modification procedure to generate valid curved meshes that have been successfully analyzed by SLAC National Accelerator Laboratory researchers to simulate the short-range wakefields in particle accelerators. The analysis results for a 8-cavity cryomodule wakefield demonstrate that valid curvilinear meshes not only make the time-domain simulations more reliable, but also improve the computational efficiency up to 30%. The application of moving curved mesh adaptation to an accelerator cavity coupler shows a tenfold reduction in execution time and memory usage without loss in accuracy as compared to uniformly refined meshes.

Identifying and Meshing Thin Sections of 3-d Curved Domains

Realization of the full benefits of variable p-version finite elements requires the careful construction of prismatic elements in thin sections. This paper presents a procedure to automatically isolate the thin sections using the points on an approximate medial surface computed by an octree-based algorithm. Using the pairs of triangles associated with medial surface (MS) points, in conjunction with adjacency, classification and distance information, sets of surface triangles that are on opposite face patches in thin sections are identified. Mesh modifications are then executed to match the surface triangulations on the opposite face patches such that prismatic elements can be generated without diagonal edges through the thickness directions.

The M3D-C1 Approach to Simulating 3D 2-fluid Magnetohydrodynamics in Magnetic Fusion Experiments

A new approach for solving the 3D MHD equations in a strongly magnetized toroidal plasma is presented which uses high-order 2D finite elements with C1 continuity. The vector fields use a physics-based decomposition. An efficient implicit time advance separates the velocity and field advance. ITAPS (SCOREC) adaptivity software and TOPS solvers are used.

Interoperable mesh and geometry tools for advanced petascale simulations

SciDAC applications have a demonstrated need for advanced software tools to manage the complexities associated with sophisticated geometry, mesh, and field manipulation tasks, particularly as computer architectures move toward the petascale. The Center for Interoperable Technologies for Advanced Petascale Simulations (ITAPS) will deliver interoperable and interchangeable mesh, geometry, and field manipulation services that are of direct use to SciDAC applications. The premise of our technology development goal is to provide such services as libraries that can be used with minimal intrusion into application codes. To develop these technologies, we focus on defining a common data model and data-structure neutral interfaces that unify a number of different services such as mesh generation and improvement, front tracking, adaptive mesh refinement, shape optimization, and solution transfer operations. We highlight the use of several ITAPS services in SciDAC applications.

Interoperable mesh components for large-scale, distributed-memory simulations

SciDAC applications have a demonstrated need for advanced software tools to manage the complexities associated with sophisticated geometry, mesh, and field manipulation tasks, particularly as computer architectures move toward the petascale. In this paper, we describe a software component – an abstract data model and programming interface – designed to provide support for parallel unstructured mesh operations. We describe key issues that must be addressed to successfully provide high-performance, distributed-memory unstructured mesh services and highlight some recent research accomplishments in developing new load balancing and MPI-based communication libraries appropriate for leadership class computing. Finally, we give examples of the use of parallel adaptive mesh modification in two SciDAC applications.

Curved mesh correction and adaptation tool to improve COMPASS electromagnetic analyses

SLAC performs large-scale simulations for the next-generation accelerator design using higher-order finite elements. This method requires using valid curved meshes and adaptive mesh refinement in complex 3D curved domains to achieve its fast rate of convergence. ITAPS has developed a procedure to address those mesh requirements to enable petascale electromagnetic accelerator simulations by SLAC. The results demonstrate that those correct valid curvilinear meshes can not only make the simulation more reliable but also improve computational efficiency up to 30%. This paper presents a procedure to track moving adaptive mesh refinement in curved domains. The procedure is capable of generating suitable curvilinear meshes to enable large-scale accelerator simulations. The procedure can generate valid curved meshes with substantially fewer elements to improve the computational efficiency and reliability of the COMPASS electromagnetic analyses. Future work will focus on the scalable parallelization of all steps for petascale simulations.

Tracking Adaptive Moving Mesh Refinements in 3D Curved Domains for Large-Scale Higher Order Finite Element Simulations

When applying higher order finite elements to curved 3D domains in large-scale accelerator simulations, complexities that arise include needing valid curved finite elements and the capability to track the movement of mesh refinement in the critical domains. This paper presents a procedure which combines Bezier mesh curving and size driven mesh adaptation technologies to address those requirements. The intelligent selection of local mesh modifications to eliminate invalid curved elements and properly control the size distribution are the two key technical components. The procedure has been successfully applied by SLAC to generate 3D moving curved meshes in the large-scale electromagnetic modeling of next generation accelerator designs. The results demonstrated that valid curvilinear meshes not only make the time domain simulations more reliable but also improve the computational efficiency up to 30%.