We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

This paper presents a computationally efficient runtime partitioning and load-balancing scheme for the Distributed Adaptive Grid Hierarchies that underlie adaptive mesh-refinement methods. The partitioning scheme yields an efficient parallel computational structure that maintains locality to reduce communications. Further, it enables dynamic re-partitioning and loadbalancing of the adaptive grid hierarchy to be performed cost-effectively. The run-time partitioning support presented has been implemented within the framework of a data-management infrastructure supporting dynamic distributed data-structures for parallel adaptive numerical techniques. This infrastructure is the foundational layer of a computational toolkit for the Binary Black-Hole NSF Grand Challenge project. 1 Introduction Dynamically adaptive methods for the solution of partial differential equations that employ locally optimal approximations can yield highly advantageous ratios for cost/accuracy when compared to metho...

Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid codes) and/or irregularly coupled (called multiblock or irregularly coupled regular mesh problems). In this paper, we present a combined runtime and compile-time approach for parallelizing these applications on distributed memory parallel machines in an efficient and machine-independent fashion. Wehave designed and implemented a runtime library which can be used to port these applications on distributed memory machines. The library is currently implemented on several different systems. To further ease the task of application programmers, wehave developed methods for integrating this runtime library with compilers for HPF-like parallel programming languages. We discuss howwehaveintegrated this runtime library with the Fortran 90D compiler being developed at Syracuse University. We present experimental results to demonstrate the efficacy of our approach. Wehave exper...

In this paper we present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advectiondiffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Our approach to adaptive refinement uses a nested hierarchy of logically-rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedur...

We discuss Inverse Spacefilling Partitioning (ISP), a partitioning strategy for nonuniform scientific computations running on distributed memory MIMD parallel computers. We consider the case of a dynamic workload distributed on a uniform mesh, and compare ISP against Orthogonal Recursive Bisection (ORB) and a Median of Medians variant of ORB, ORB-MM. We present two results. First, ISP and ORB-MM are superior to ORB in rendering balanced workloads---because they are more finegrained ---and incur communication overheads that are comparable to ORB. Second, ISP is more attractive than ORB-MM from a software engineering standpoint because it avoids elaborate bookkeeping. Whereas ISP partitionings can be described succinctly as logically contiguous segments of the line, ORB-MM's partitionings are inherently unstructured. We describe the general d-dimensional ISP algorithm and report empirical results with two- and three-dimensional, non-hierarchical particle methods. Scott B. Bad...

this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.

LPARX provides efficient run-time support for dynamic, non-uniform scientific calculations running on MIMD distributed memory architectures. It extends HPF's data decomposition model to provide support for dynamic, block irregular data structures. LPARX represents data decompositions as first-class objects and expresses data dependencies in a manner which is logically independent of data decomposition and problem dimension. LPARX applications are portable across a diversity of MIMD machines. We have implemented a number of applications in LPARX--- including a 3d particle calculation and 2d and 3d adaptive multigrid solvers---which could not have been efficiently implemented in HPF.

Conservation laws ae solved by a local Gaerkin finite element procedure with adapfive space-time mesh refinement ad explicit time integration. The Courat stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. Processor load imbalaces, introduced at adaptive enrichment steps, are corrected by using traversals of an octtee representing a spatial decomposition of the domain. To accommodate the variable time steps, octtee partitioning is extended to use weights derived from element size. Partition boundary smoothing reduces the communications volume of partitioning procedures for a modest cost. Computational results comparing parallel octtee ad inertial partitioning procedures ae presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer.

Understanding the most efficient design and utilization of emerging multicore systems is one of the most challenging questions faced by the mainstream and scientific computing industries in several decades. Our work explores multicore stencil (nearest-neighbor) computations — a class of algorithms at the heart of many structured grid codes, including PDE solvers. We develop a number of effective optimization strategies, and build an auto-tuning environment that searches over our optimizations and their parameters to minimize runtime, while maximizing performance portability. To evaluate the effectiveness of these strategies we explore the broadest set of multicore architectures in the current HPC literature, including the

Adaptive local grid refinement/coarsening results in unequal distribution of workload among the processors of a parallel system. A novel method for balancing the load in cases of dynamically changing tetrahedral grids is developed. The approach Graduate Research Assistant, Dept. of Electrical and Computer Engineering y Assistant Professor, Member AIAA z Research Scientist, Member AIAA 1 employs local exchange of cells among processors in order to redistribute the load equally. An important part of the load balancing algorithm is the method employed by a processor to determine which cells within its subdomain are to be exchanged. Two such methods are presented and compared. The strategy for load balancing is based on the Divide-and-Conquer approach which leads to an efficient parallel algorithm. This method is implemented on a distributed-memory MIMD system. 1 Introduction Computational fluid dynamics (CFD) has advanced rapidly over the last two decades and it is recognized as a...