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27
Terrain Simplification Simplified: A General Framework for ViewDependent OutofCore Visualization
, 2002
"... This paper describes a general framework for outofcore rendering and management of massive terrain surfaces. The two key components of this framework are: viewdependent refinement of the terrain mesh; and a simple scheme for organizing the terrain data to improve coherence and reduce the number o ..."
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Cited by 81 (2 self)
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This paper describes a general framework for outofcore rendering and management of massive terrain surfaces. The two key components of this framework are: viewdependent refinement of the terrain mesh; and a simple scheme for organizing the terrain data to improve coherence and reduce the number of paging events from external storage to main memory. Similar to several previously proposed methods for viewdependent refinement, we recursively subdivide a triangle mesh defined over regularly gridded data using longestedge bisection. As part of this single, perframe refinement pass, we perform triangle stripping, view frustum culling, and smooth blending of geometry using geomorphing. Meanwhile, our refinement framework supports a large class of error metrics, is highly competitive in terms of rendering performance, and is surprisingly simple to implement. Independent
Global Static Indexing for Realtime Exploration of Very Large Regular Grids
, 2001
"... In this paper we introduce a new indexing scheme for progressive traversal and visualization of large regular grids. We demonstrate the potential of our approach by providing a tool that displays at interactive rates planar slices of scalar field data with very modest computing resources. We obtain ..."
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Cited by 44 (7 self)
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In this paper we introduce a new indexing scheme for progressive traversal and visualization of large regular grids. We demonstrate the potential of our approach by providing a tool that displays at interactive rates planar slices of scalar field data with very modest computing resources. We obtain unprecedented results both in terms of absolute performance and, more importantly, in terms of scalability. On a laptop computer we provide real time interaction with a 2048 3 grid (8 Giganodes) using only 20MB of memory. On an SGI Onyx we slice interactively an 8192 3 grid ( teranodes) using only 60MB of memory. The scheme relies simply on the determination of an appropriate reordering of the rectilinear grid data and a progressive construction of the output slice. The reordering minimizes the amount of I/O performed during the outofcore computation. The progressive and asynchronous computation of the output provides flexible quality/speed tradeoffs and a timecritical and interruptible user interface. 1.
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences
, 1998
"... We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which is constructed from a onedimensional multiscale basis by the tensor product approach. Together with the use of hash tables as data structure, this allows in a simple way for a ..."
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Cited by 29 (15 self)
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We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which is constructed from a onedimensional multiscale basis by the tensor product approach. Together with the use of hash tables as data structure, this allows in a simple way for adaptive refinement and is, due to the tensor product approach, well suited for higher dimensional problems. Also, the adaptive treatment of partial differential equations, the discretization (involving finite differences) and the solution (here by preconditioned BiCG) can be programmed easily. We describe the basic features of the method, discuss the discretization, the solution and the refinement procedures and report on the results of different numerical experiments.
Multiresolution Visualization and Compression Of Global . . .
 GEOINFORMATICA
, 1999
"... We present a multiresolution model for surfaces which is able to handle largescale global topographic data. It is based on a hierarchical decomposition of the sphere by a recursive bisection triangulation in geographic coordinates. Error indicators allow the representation of the data at various ..."
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Cited by 18 (2 self)
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We present a multiresolution model for surfaces which is able to handle largescale global topographic data. It is based on a hierarchical decomposition of the sphere by a recursive bisection triangulation in geographic coordinates. Error indicators allow the representation of the data at various levels of detail and enable data compression by local omission of data values. The resulting hierarchical triangulation is stored using a bit code of the underlying binary tree and, additionally, relative pointers which allow an adaptive tree traversal. This way, it is possible to work directly on the compressed data. We show that significant compression rates can be obtained already for small threshold values. In a visualization application, adaptive triangulations which consist of hundreds of thousands of shaded triangles are extracted and drawn at interactive rates.
Balanced refinement of massive linear octrees
, 2004
"... This paper presents a solution to the problem of balance refinement of massive linear octrees. We combine existing database techniques (Btree, bulk loading, and range queries) with new algorithms (balance by parts, prioritized ripple propagation) and data structures (the cache octree) into a unifie ..."
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Cited by 10 (8 self)
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This paper presents a solution to the problem of balance refinement of massive linear octrees. We combine existing database techniques (Btree, bulk loading, and range queries) with new algorithms (balance by parts, prioritized ripple propagation) and data structures (the cache octree) into a unified framework that provides new capabilities for large scientific applications. 1
Parallel AMG on Distributed Memory Computers
, 2000
"... Algebraic Multigrid (AMG) methods are well suited as preconditioners for iterative solvers of linear systems of equations which are sparse, symmetric positive definite and stem from a finite element (FE) discretization of a 2 nd order elliptic partial differential equation (PDE) or a system of PDE ..."
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Cited by 8 (5 self)
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Algebraic Multigrid (AMG) methods are well suited as preconditioners for iterative solvers of linear systems of equations which are sparse, symmetric positive definite and stem from a finite element (FE) discretization of a 2 nd order elliptic partial differential equation (PDE) or a system of PDEs. Since preconditioners based on AMG are very efficient, additional speedup can only be achieved by parallelization. In this paper we propose a general parallel AMG algorithm which is well suited for distributed memory computers. The algorithm is based on domain decomposition ideas and allows overlapping and nonoverlapping data decompositions. This paper pays special attention to the coarsening strategy which has to be adapted in the parallel case. Moreover, a general framework of data distribution gives rise to a construction scheme for the prolongation operators. Results of numerical studies on parallel machines with distributed memory are presented which show the high efficiency of the ...
On the Quality of Partitions based on SpaceFilling Curves
, 2002
"... This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times ..."
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Cited by 6 (1 self)
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This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 3 times larger than the optimal in average case.
Parallelization of irregular problems based on hierarchical domain representation
 Proceedings of HPCN 2000: Lecture
, 2000
"... Abstract. Irregular problems require the computation of some properties for a set of elements that are irregularly distributed in a domain. The distribution may change at run time in a way that cannot be foreseen in advance. Most irregular problems satisfy a locality property because the properties ..."
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Cited by 5 (4 self)
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Abstract. Irregular problems require the computation of some properties for a set of elements that are irregularly distributed in a domain. The distribution may change at run time in a way that cannot be foreseen in advance. Most irregular problems satisfy a locality property because the properties of an element e depend on the elements that are ”close ” to e. We propose a methodology to develop a highly parallel solution based upon a load balancing strategy that respects locality because e and most of the elements close to e are mapped onto the same processing node. We also discuss the update of the mapping at run time to recover an unbalancing, together with strategies to acquire data on elements mapped onto other processing node. The proposed methodology is applied to the multigrid adaptive problem and some experimental results are discussed. 1
Parallel multigrid summation for the Nbody problem
, 2004
"... A Θ(n) parallel multigrid summation method for the Nbody problem is presented. The method works with vacuum or periodic boundary conditions. It is based on a hierarchical decomposition of computational kernels on multiple grids. For low accuracy calculations, appropriate for molecular dynamic ..."
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Cited by 5 (0 self)
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A Θ(n) parallel multigrid summation method for the Nbody problem is presented. The method works with vacuum or periodic boundary conditions. It is based on a hierarchical decomposition of computational kernels on multiple grids. For low accuracy calculations, appropriate for molecular dynamics, a sequential implementation is faster than both Fast Multipole and Particle Mesh Ewald (PME). Its parallel implementation is more scalable than PME and comparable to the fast multipole. The method can be combined with multiple time stepping integrators to produce a powerful simulation protocol for simulation of biological molecules and other materials. The parallel implementation is based on MPI, and is tested in a variety of clusters and shared memory computers. It is available as opensource in http://protomol.sourceforge.net. An auxiliary tool allows the automatic selection of optimal parameters for given molecular systems and accuracies required, and is available in http://mdsimaid.cse.nd.edu.
A parallel Vlasov solver using a wavelet based adaptive mesh refinement
 In 7th Workshop on High Perf. Scientific and Engineering Computing (ICPP’2005
, 2005
"... We are interested in solving the Vlasov equation used to describe collective effects in plasmas. This nonlinear partial differential equation coupled with Maxwell equation describes the time evolution of the particle distribution in phase space. The numerical solution of the full threedimensional V ..."
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Cited by 5 (1 self)
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We are interested in solving the Vlasov equation used to describe collective effects in plasmas. This nonlinear partial differential equation coupled with Maxwell equation describes the time evolution of the particle distribution in phase space. The numerical solution of the full threedimensional VlasovMaxwell system represents a considerable challenge due to the huge size of the problem. A numerical method based on wavelet transform enables to compute the distribution function on an adaptive mesh from a regular discretization of the phase space. In this paper, we evaluate the costs of this recently developed adaptive scheme applied on a reduced onedimensional model, and its parallelization. We got a fine grain parallel application that achieves a good scalability up to 64 processors on a shared memory architecture. 1