相关论文: Efficient cache use for stencil operations on stru…

A number of known techniques for improving cache performance in scientific computations involve the reordering of the iteration space. Some of these reorderings can be considered coverings of the iteration space with sets having small…

Stencil computations on low dimensional grids are kernels of many scientific applications including finite difference methods used to solve partial differential equations. On typical modern computer architectures, such stencil computations…

Stencil computations lie at the heart of many scientific and industrial applications. Unfortunately, stencil algorithms perform poorly on machines with cache based memory hierarchy, due to low re-use of memory accesses. This work shows that…

Stencil computations are widely used in HPC applications. Today, many HPC platforms use GPUs as accelerators. As a result, understanding how to perform stencil computations fast on GPUs is important. While implementation strategies for…

Good process-to-compute-node mappings can be decisive for well performing HPC applications. A special, important class of process-to-node mapping problems is the problem of mapping processes that communicate in a sparse stencil pattern to…

Stencils represent a class of computational patterns where an output grid point depends on a fixed shape of neighboring points in an input grid. Stencil computations are prevalent in scientific applications engaging a significant portion of…

It is well known that to accelerate stencil codes on CPUs or GPUs and to exploit hardware caches and their lines optimizers must find spatial and temporal locality of array accesses to harvest data-reuse opportunities. On FPGAs there is the…

Unfitted boundary methods are widely used to numerically solve partial differential equations (PDEs) on irregular domains, avoiding the computational burden of generating boundary-conforming grids. In the finite-difference framework,…

Stencil computation is one of the most used kernels in a wide variety of scientific applications, ranging from large-scale weather prediction to solving partial differential equations. Stencil computations are characterized by three unique…

Stencil computations are a key class of applications, widely used in the scientific computing community, and a class that has particularly benefited from performance improvements on architectures with high memory bandwidth. Unfortunately,…

We introduce a geometric stencil selection algorithm for Laplacian in 3D that significantly improves octant-based selection considered earlier. The goal of the algorithm is to choose a small subset from a set of irregular points surrounding…

An out-of-core stencil computation code handles large data whose size is beyond the capacity of GPU memory. Whereas, such an code requires streaming data to and from the GPU frequently. As a result, data movement between the CPU and GPU…

This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…

Bandwidth-starved multicore chips have become ubiquitous. It is well known that the performance of stencil codes can be improved by temporal blocking, lessening the pressure on the memory interface. We introduce a new pipelined approach…

Optimizing the performance of stencil algorithms has been the subject of intense research over the last two decades. Since many stencil schemes have low arithmetic intensity, most optimizations focus on increasing the temporal data access…

We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…

This dissertation develops hardware that automatically reduces the effective latency of accessing memory in both single-core and multi-core systems. To accomplish this, the dissertation shows that all last level cache misses can be…

Stencil computations are a fundamental kernel in scientific computing, critical for simulations in domains such as fluid dynamics and climate modeling. However, these computations are often memory-bound on traditional High-Performance…

By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…