Special Session 115: Computational Techniques Using Fast Fourier Transformation (FFT) for Partial Differential Equations

Advancements in FFT Techniques: A Focus on My Publications

Samar Aseeri King Abdullah University of Science and Technology Saudi Arabia Co-Author(s):    Benson Muite & David Keyes

Abstract: This presentation will focus on my publications related to Fast Fourier Transforms (FFTs) and their applications in solving Partial Differential Equations (PDEs). I will discuss significant advancements in parallel FFT techniques and benchmarking practices, showcasing how these contributions enhance the efficiency and accuracy of complex PDE solutions. By sharing insights from my research, I aim to foster collaboration and knowledge exchange among participants. Attendees will gain a deeper understanding of the implications of FFT methodologies in computational techniques and mathematical modeling.

Utilizing Network Delays for Modeling Physical Propagation in HPC

Anando G Chatterjee Indian Institute of Technology Kanpur India Co-Author(s):

Abstract: A common trend in high-performance computing (HPC) is the effort to minimize network delays to enhance performance. However, in compressible fluids, disturbances originating in one region propagate through the medium at the speed of sound, with other regions evolving independently until the disturbance reaches them. Similarly, in HPC environments, signals travel across the network at the speed of electromagnetic waves (i.e., the speed of light). In this work, we explore an approach that draws an analogy between these two systems by intentionally mapping the physical propagation delays to the network delays. This novel perspective seeks to align computation with communication delays, leveraging the inherent latency of the network rather than eliminating it, thus optimizing both system behavior and performance.

An Efficient Algorithm for Region-Based Image Segmentation using Phase Field Functions

Gunay Dogan National Institute of Standards and Technology USA Co-Author(s):    Harbir Antil, Soeren Bartels

Abstract: Image segmentation is the task of finding objects or regions in given images, and is a fundamental problem in computer vision. In this work, We propose a new model for region-based image segmentation. Our model provides a background-foreground segmentation like the Chan-Vese model. An important feature of our model is a novel regularization term that leverages fractional diffusion for improved regularization of region boundaries. Fractional diffusion is much gentler compared to the curve length penalty typically used in similar models, and this leads to improved recovery of geometric details on region boundaries. We model the regions using a phase field function, and discretize the problem with a spectral approximation. Solving the problem requires an energy minimization via gradient descent evolution of the phase field function. This is realized with an implicit-explicit Euler time discretization of the evolution equation. Each iteration step of this evolution requires only two Fast Fourier Transforms. We demonstrate the effectiveness of our algorithm with several examples.

Spectral methods for nonlinear dispersive equations

Christian Klein University of Burgundy France Co-Author(s):    N. Stoilov

Abstract: Nonlinear dispersive equations are omnipresent in applications in hydrodynamics, nonlinear optics, plasma physics,... but their mathematical description is challenging since they can have stable solitary waves, but also zones of rapid modulated oscillations called dispersive shock waves and even a blow-up, a loss of regularity in finite time. For the numerical description spectral methods are the preferred choice since they minimise the introduction of numerical dissipation which could suppress the dispersive effects to be studied. For smooth rapidly decreasing or periodic functions, FFT techniques are preferred. But we will also discuss spectral methods, for instance Chebyshev polynomials, for slowly decaying or piecewise smooth functions. Several examples are discussed, also for fractional derivatives.

Implementation of Parallel 3-D Real FFT with 2-D Decomposition on Manycore Clusters

Daisuke Takahashi University of Tsukuba Japan Co-Author(s):    Daisuke Takahashi

Abstract: In this talk, we propose an implementation of parallel three-dimensional real fast Fourier transforms (FFTs) with two-dimensional decomposition on manycore clusters. The proposed parallel three-dimensional FFT algorithm is based on the conjugate symmetry property for the discrete Fourier transform (DFT) and the multicolumn FFT algorithm. We show that a two-dimensional decomposition effectively improves performance by reducing the communication time for larger numbers of MPI processes. We also present a computation-communication overlap method that introduces a communication thread with OpenMP. Performance results of three-dimensional real FFTs on manycore clusters are reported.