Related papers: Tight Bounds for Low Dimensional Star Stencils in …
Stencil computation is one of the most widely-used compute patterns in high performance computing applications. Spatial and temporal blocking have been proposed to overcome the memory-bound nature of this type of computation by moving…
Although modern supercomputers are composed of multicore machines, one can find scientists that still execute their legacy applications which were developed to monocore cluster where memory hierarchy is dedicated to a sole core. The main…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
Stencil computations, involving operations over the elements of an array, are a common programming pattern in scientific computing, games, and image processing. As a programming pattern, stencil computations are highly regular and amenable…
We introduce QPU micro-kernels: shallow quantum circuits that perform a stencil node update and return a Monte Carlo estimate from repeated measurements. We show how to use them to solve Partial Differential Equations (PDEs) explicitly…
Current architectures are now equipped with matrix computation units designed to enhance AI and high-performance computing applications. Within these architectures, two fundamental instruction types are matrix multiplication and vector…
In this paper we evaluate the performance of FPGAs for high-order stencil computation using High-Level Synthesis. We show that despite the higher computation intensity and on-chip memory requirement of such stencils compared to first-order…
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…
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…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
As investment in AI-focused accelerators grows and their deployment in supercomputing facilities expands, understanding whether these architectures can efficiently support traditional scientific kernels is critical for the future of…
In this paper, we study the static cell probe complexity of non-adaptive data structures that maintain a subset of $n$ points from a universe consisting of $m=n^{1+\Omega(1)}$ points. A data structure is defined to be non-adaptive when the…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
A {\em Steiner star} for a set $P$ of $n$ points in $\RR^d$ connects an arbitrary center point to all points of $P$, while a {\em star} connects a point $p\in P$ to the remaining $n-1$ points of $P$. All connections are realized by straight…
When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
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…
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…
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,…
Emerging hybrid accelerator architectures for high performance computing are often suited for the use of a data-parallel programming model. Unfortunately, programmers of these architectures face a steep learning curve that frequently…