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We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…

Optimization and Control · Mathematics 2017-02-01 F. Yang , C. Venkataraman , V. Styles , A. Madzvamuse

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…

Computational Physics · Physics 2020-06-24 Niklas Fehn , Peter Munch , Wolfgang A. Wall , Martin Kronbichler

We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios…

Optimization and Control · Mathematics 2023-10-17 Minseok Ryu , Geunyeong Byeon , Kibaek Kim

The kernel-free boundary integral (KFBI) method has successfully solved partial differential equations (PDEs) on irregular domains. Diverging from traditional boundary integral methods, the computation of boundary integrals in KFBI is…

Numerical Analysis · Mathematics 2024-04-24 Liwei Tan , Minsheng Huang , Wenjun Ying

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel…

Optimization and Control · Mathematics 2023-05-26 Di Zhang , Xiaoya Zhai , Ligang Liu , Xiao-Ming Fu

We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…

Machine Learning · Computer Science 2017-11-08 Celestine Dünner , Thomas Parnell , Martin Jaggi

The torrential influx of floating-point data from domains like IoT and HPC necessitates high-performance lossless compression to mitigate storage costs while preserving absolute data fidelity. Leveraging GPU parallelism for this task…

Databases · Computer Science 2025-11-12 Zheng Li , Weiyan Wang , Ruiyuan Li , Chao Chen , Xianlei Long , Linjiang Zheng , Quanqing Xu , Chuanhui Yang

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

Materials Science · Physics 2022-11-24 Vir Karan , A. Maruthi Indresh , Saswata Bhattacharyya

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…

Machine Learning · Computer Science 2023-04-05 Cosmas Heiß , Ingo Gühring , Martin Eigel

A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…

Numerical Analysis · Mathematics 2020-05-13 Jun Hu , Hua Wang

We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical…

Numerical Analysis · Mathematics 2025-07-02 Youngkyu Lee , Shanqing Liu , Jerome Darbon , George Em Karniadakis

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-24 Ioannis Sakiotis , Kamesh Arumugam , Marc Paterno , Desh Ranjan , Balša Terzić , Mohammad Zubair

Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…

Numerical Analysis · Mathematics 2025-12-10 Teoman Toprak , Florian Kummer

The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…

Mathematical Software · Computer Science 2018-03-08 Andrew Reisner , Luke N. Olson , J. David Moulton

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Numerical Analysis · Mathematics 2024-05-10 Yan Xie , Minrui Lv , Chensong Zhang

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems…

In this work we propose an accelerated stochastic learning system for very large-scale applications. Acceleration is achieved by mapping the training algorithm onto massively parallel processors: we demonstrate a parallel, asynchronous GPU…

Machine Learning · Computer Science 2017-02-24 Thomas Parnell , Celestine Dünner , Kubilay Atasu , Manolis Sifalakis , Haris Pozidis

At the heart of the Met Office climate and weather forecasting capabilities lies a sophisticated numerical model which solves the equations of large-scale atmospheric flow. Since this model uses semi-implicit time-stepping, it requires the…

Computational Physics · Physics 2023-11-27 Andrew Malcolm , Eike H. Müller , Robert Scheichl

To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…

Computational Engineering, Finance, and Science · Computer Science 2021-04-29 Zhenqi Wang , Sebastian Wende-von Berg , Martin Braun

Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…

Computational Physics · Physics 2020-04-01 V. Florinski , D. S. Balsara , S. Garain , K. F. Gurski