Publications/Algorithms

MACH-B: Fast Multipole Method Approaches in Particle Accelerator Simulations for the Computational and Intensity Frontiers

The MACH-B (Multipole Accelerator Codes for Hadron Beams) project is developing a Fast Multipole Method [1–7] (FMM)-based tool for higher fidelity modeling of particle accelerators for high-energy physics within the next generation of Fermilab’s Synergia simulation package [8]. MACH-B incorporates (1) highly-scalable, high-performance and generally-applicable FMM-based algorithms [5–7, 9] to

05/27/2021

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to

09/22/2020

On the Bottleneck Structure of Congestion-Controlled Networks

In this paper, we introduce the Theory of Bottleneck Ordering, a mathematical framework that reveals the bottleneck structure of data networks. This theoretical framework provides insights into the inherent topological properties of a network at least in three areas: (1) It identifies the regions of influence of each bottleneck; (2)

06/08/2020

Low-Frequency Electromagnetic Imaging Using Sensitivity Functions and Beamforming

We present a computational technique for low-frequency electromagnetic imaging in inhomogeneous media that provides superior three-dimensional resolution over existing techniques. The method is enabled through large-scale, fast (low-complexity) algorithms that we introduce for simulating electromagnetic wave propagation. We numerically study the performance of the technique on various problems including the

05/05/2020

Systems and Methods for Efficient Targeting

A system for determining the physical path of an object can map several candidate paths to a suitable path space that can be explored using a convex optimization technique. The optimization technique may take advantage of the typical sparsity of the path space and can identify a likely physical path

11/05/2019

Fast Large-Scale Algorithm for Electromagnetic Wave Propagation in 3D Media

We present a fast, large-scale algorithm for the simulation of electromagnetic waves (Maxwell’s equations) in three-dimensional inhomogeneous media. The algorithm has a complexity of O(N log(N)) and runs in parallel. Numerical simulations show the rapid treatment of problems with tens of millions of unknowns on a small shared-memory cluster (

09/24/2019

Combinatorial Multigrid: Advanced Preconditioners For Ill-Conditioned Linear Systems

The Combinatorial Multigrid (CMG) technique is a practical and adaptable solver and combinatorial preconditioner for solving certain classes of large, sparse systems of linear equations. CMG is similar to Algebraic Multigrid (AMG) but replaces large groupings of fine-level variables with a single coarse-level one, resulting in simple and fast interpolation

09/24/2019

Systems and Methods for Multiresolution Parsing

A multiresolution parser (MRP) can selectively extract one or more information units from a dataset based on the available processing capacity and/or the arrival rate of the dataset. Should any of these parameters change, the MRP can adaptively change the information units to be extracted such that the benefit or

06/04/2019

On the Bottleneck Structure of Positive Linear Programming

Positive linear programming (PLP), also known as packing and covering linear programs, is an important class of problems frequently found in fields such as network science, operations research, or economics. In this work we demonstrate that all PLP problems can be represented using a network structure, revealing new key insights

05/23/2019

MACH-B: Fast Multipole Method Approaches in Particle Accelerator Simulations for the Computational and Intensity Frontiers

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

On the Bottleneck Structure of Congestion-Controlled Networks

Low-Frequency Electromagnetic Imaging Using Sensitivity Functions and Beamforming

Systems and Methods for Efficient Targeting

Fast Large-Scale Algorithm for Electromagnetic Wave Propagation in 3D Media

Combinatorial Multigrid: Advanced Preconditioners For Ill-Conditioned Linear Systems

Systems and Methods for Multiresolution Parsing

On the Bottleneck Structure of Positive Linear Programming

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