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Commonrefinementbased data transfer between nonmatching meshes in multiphysics simulations
 International Journal for Numerical Methods in Engineering
, 2004
"... In multiphysics simulations using a partitioned approach, each physics component solves on its own mesh, and the interfaces between these meshes are in general nonmatching. Simulation data (e.g. jump conditions) must be exchanged across the interface meshes between physics components. It is highly ..."
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In multiphysics simulations using a partitioned approach, each physics component solves on its own mesh, and the interfaces between these meshes are in general nonmatching. Simulation data (e.g. jump conditions) must be exchanged across the interface meshes between physics components. It is highly desirable for such data transfers to be both numerically accurate and physically conservative. This paper presents accurate, conservative, and efficient data transfer algorithms utilizing a common refinement of two nonmatching surface meshes. Our methods minimize errors in a certain norm while achieving strict conservation. Some traditional methods for data transfer and related problems are also reviewed and compared with our methods. Numerical results demonstrate significant advantages of commonrefinement based methods, especially for repeated transfers. While the comparisons are performed with matching geometries, this paper also addresses additional complexities associated with nonmatching surface meshes and presents some experimental results from 3D simulations using our
Local polyhedra and geometric graphs
 In Proc. 14th ACMSIAM Sympos. on Discrete Algorithms
, 2003
"... We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest ed ..."
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We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest edges differ by at most a polynomial factor. A polyhedron is local if all its faces are simplices and its edges form a local geometric graph. We show that any boolean combination of any two local polyhedra in IR d each with n vertices, can be computed in O(n log n) time, using a standard hierarchy of axisaligned bounding boxes. Using results of de Berg, we also show that any local polyhedron in IR d has a binary space partition tree of size O(n log d1 n). Finally, we describe efficient algorithms for computing Minkowski sums of local polyhedra in two and three dimensions.
Overlaying surface meshes, part I: Algorithms
 INT. J. COMPUT. GEOM. APPL.
, 2004
"... We describe an efficient and robust algorithm for computing a common refinement of two meshes modeling the same surface of arbitrary shape by overlaying them on lop of each other. A common refinement is an important data structure for transferring data between meshes that have different combinatoria ..."
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Cited by 5 (1 self)
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We describe an efficient and robust algorithm for computing a common refinement of two meshes modeling the same surface of arbitrary shape by overlaying them on lop of each other. A common refinement is an important data structure for transferring data between meshes that have different combinatorial structures. Our algorithm is optimal in time and space, with linear complexity, and is robust even with inexact computations, through the techniques of error analysis, detection of topological inconsistencies, and automatic resolution of such inconsistencies. We present the verification and some further enhancement of robustness in Part II.
A.: Virtual Prototyping of Solid Propellant Rockets
 Computing in Science and Engineering
, 2000
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A New Approach to Software Integration Frameworks for Multiphysics Simulation Codes
, 2000
"... Existing software integration frameworks typically require large manual rewrites of existing codes, or specific tailoring of codes written to be used in the framework. The result is usually a specialpurpose code which is not usable outside of the framework. In this paper, we propose an alternativ ..."
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Cited by 3 (0 self)
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Existing software integration frameworks typically require large manual rewrites of existing codes, or specific tailoring of codes written to be used in the framework. The result is usually a specialpurpose code which is not usable outside of the framework. In this paper, we propose an alternative to that model  a framework that requires little handmodification of the programs which use it. Our proposed framework is meshaware, numericsaware, and physicsaware. This makes it possible to move some of the difficulties of interfacing simulation codes out of the codes themselves, and into the framework, while the internal parallelization, communication and numerical solution methods are left intact. Descriptions of the codes and the orchestration of the system, make it possible to automatically translate the simulation source code into a form that can fit into the framework. We report on some preliminary experiments with an automatic load balancing framework that demonstrate the feasibility of this approach. 1
Efficient and robust algorithm for overlaying nonmatching surface meshes
 IN 10TH INTERNATIONAL MESHING ROUNDTABLE
, 2001
"... This paper describes an efficient and robust algorithm for computing a common refinement of two meshes modeling a common surface of arbitrary shape by overlaying them on top of each other. A common refinement is an important data structure for transferring data between meshes that have different top ..."
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Cited by 2 (2 self)
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This paper describes an efficient and robust algorithm for computing a common refinement of two meshes modeling a common surface of arbitrary shape by overlaying them on top of each other. A common refinement is an important data structure for transferring data between meshes that have different topological structures. Our algorithm is optimal in time and space, with linear complexity. Special treatments are introduced to handle discretization and rounding errors and to ensure robustness with imprecise computations. It also addresses the additional complexities caused by degeneracies, sharp edges, sharp corners, and nonmatching boundaries. The algorithm has been implemented and demonstrated to be robust for complex geometries from realworld applications.
Coupled fluidstructure 3D solid rocket motor simulations
 In 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference
"... We describe our numerical method for threedimensional simulations of solid rocket motors in which the internal gas dynamics, the combustion of the propellant, and the structural response are fully coupled. The combustion zone is treated as a thin layer using appropriate jump conditions, and the regr ..."
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Cited by 1 (1 self)
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We describe our numerical method for threedimensional simulations of solid rocket motors in which the internal gas dynamics, the combustion of the propellant, and the structural response are fully coupled. The combustion zone is treated as a thin layer using appropriate jump conditions, and the regression rate is determined using a nonlinear dynamic combustion model. An Arbitrary LagrangianEulerian formulation is used in the gas dynamics and structural mechanics modules to follow the regression of the propellant. We demonstrate the parallel scalability of our ALE implementation and its ability to handle significant burn back of the propellant on a model problem with a very high burn rate.
Local Polyhedra and Geometric Graphs*
"... Local Polyhedra and Geometric Graphs 1 1 Introduction Nonconvex polyhedra are ubiquitous in computer graphics, solid modeling, computer aided design and manufacturing, robotics, and other geometric application areas. Unlike nonconvex polygons or convex objects in space, for which many problems can b ..."
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Local Polyhedra and Geometric Graphs 1 1 Introduction Nonconvex polyhedra are ubiquitous in computer graphics, solid modeling, computer aided design and manufacturing, robotics, and other geometric application areas. Unlike nonconvex polygons or convex objects in space, for which many problems can be solved easily, polyhedra are notoriously difficult to handle efficiently, at least in the worst case.