This paper describes a general framework for out-of-core rendering and management of massive terrain surfaces. The two key components of this framework are: view-dependent 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 longest-edge bisection. As part of this single, per-frame 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

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 Giga-nodes) using only 20MB of memory. On an SGI Onyx we slice interactively an 8192 3 grid ( tera-nodes) 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 out-of-core computation. The progressive and asynchronous computation of the output provides flexible quality/speed tradeoffs and a timecritical and interruptible user interface. 1.

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.

We present a multiresolution model for surfaces which is able to handle large-scale 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.

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 non-overlapping 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 ...

This paper presents a solution to the problem of balance refinement of massive linear octrees. We combine existing database techniques (B-tree, 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

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.

this memory is very limited. There is support for scatter and gather operations. Furthermore there are no operating system (OS) calls involved during communication, which could slow down the protocol. The API allows complete user access and control of the hardware. There is no support for multitasking, multi-processors or multi-protocol features. It monopolizes the NIC on the computer, resets it and reloads the control code for the NIC processor. Any other process, which accesses the NIC at the same time, may corrupt the data transfer. Such a process could also sniff into all messages processes by the NIC and it could reload the control program to access the memory of the other process. Hence it is not secure in a Unix environment. An extension of the Myricom API is the message passing system `GM' by Myricom [Myr97]. Sensitive parts of GM have been put into the kernel's Myrinet device driver. The system becomes secure and multitasking safe. The GM protocol is reliable with an acknowledge mechanism. Different processes can reserve a share of the buffer memory. The OS performs the necessary security checks. The buffer memory does not have to be contiguous memory as for the Myricom API, because page address translation is done by the OS. The routing is done by the host processors instead of the NIC processors, in order to save buffer memory on the NICs. Another extension of the Myricom API is the message passing protocol `PM' [THI96]. The send and receive buffers are still located in special contiguous memory. However, the buffers are managed by PM, rather than the user process. Packet routing is done by the host process with static routing tables. Furthermore multi-cast features have been added to the system. PM has been optimized further for performance. On top of PM the...

A Θ(n) parallel multigrid summation method for the N-body 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 open-source 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.

this paper we present results obtained using wavelet methods for the analysis and simulation of two-dimensional turbulence, and a preliminary study of a three-dimensional turbulent channel flow. The two-dimensional results show the efficiency of wavelets for the numerical simulation of turbulence, and suggest new methods for modelling the flow, based on a decomposition into coherent and incoherent parts. The three-dimensional study compares different wavelet type approaches applied to instantaneous velocity, vorticity and pressure fields. At least for the data and the setting considered in our experiments, i.e. flows with dominating boundary layer, the results indicate which of the various forms of the three-dimensional Navier--Stokes Equations (3D-NSE) (primitive variables, vorticity-streamfunction formulation) and which multiscale approach is well suited for the numerical integration of the 3D-NSE. In addition, we present efficient techniques for the implementation and parallelization of an adaptive wavelet-based 3D-NSE solver.