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Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…

Numerical Analysis · Mathematics 2018-01-26 Quan M. Bui , Howard C. Elman , J. D. Moulton

To improve the computational efficiency of heat transfer topology optimization, a Multigrid Assisted Reanalysis (MGAR) method is proposed in this study. The MGAR not only significantly improves the computational efficiency, but also…

Computational Engineering, Finance, and Science · Computer Science 2022-10-04 Jichao Yin , Hu Wang , Daozhen Guo , Shuhao Li

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…

Computational Physics · Physics 2018-07-17 Michael Lubasch , Pierre Moinier , Dieter Jaksch

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

Numerical Analysis · Mathematics 2026-01-01 Paola F. Antonietti , Matteo Caldana , Lorenzo Gentile , Marco Verani

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…

Mathematical Software · Computer Science 2020-06-19 Charles D. Murray , Tobias Weinzierl

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points.…

Numerical Analysis · Mathematics 2022-07-01 Andrey Prokopenko , Raymond S. Tuminaro

The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction $\Pi$ will…

Numerical Analysis · Mathematics 2024-01-17 Ben S. Southworth , Thomas A. Manteuffel

Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…

Numerical Analysis · Mathematics 2019-02-15 James Brannick , Scott P. MacLachlan , Jacob B. Schroder , Ben S. Southworth

Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their…

Numerical Analysis · Mathematics 2023-08-23 Tareq Zaman , Nicolas Nytko , Ali Taghibakhshi , Scott MacLachlan , Luke Olson , Matthew West

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

Numerical Analysis · Mathematics 2022-05-31 Victor A. Paludetto Magri , Robert D. Falgout , Ulrike M. Yang

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…

Machine Learning · Computer Science 2020-09-25 Ilay Luz , Meirav Galun , Haggai Maron , Ronen Basri , Irad Yavneh

Achieving the economical and stable operation of Multi-microgrids (MMG) systems is vital. However, there are still some challenging problems to be solved. Firstly, from the perspective of stable operation, it is necessary to minimize the…

Systems and Control · Electrical Eng. & Systems 2023-07-03 Yijian Wang , Yang Cui , Yang Li , Yang Xu

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…

General Finance · Quantitative Finance 2015-03-17 Edward Hoyle , Lane P. Hughston , Andrea Macrina

Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…

Numerical Analysis · Mathematics 2025-06-30 Yi Zong , Peinan Yu , Haopeng Huang , Zhengding Hu , Xinliang Wang , Qin Wang , Chensong Zhang , Xiaowen Xu , Jian Sun , Yongxiao Zhou , Wei Xue

Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…

Mathematical Software · Computer Science 2020-07-02 Sashikumaar Ganesan , Manan Shah

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…

Numerical Analysis · Mathematics 2022-04-25 Pasqua D'Ambra , Fabio Durastante , Salvatore Filippone

This paper investigates a specific instance of the static repositioning problem within station-based bike-sharing systems. Our study incorporates operational and damaged bikes, a heterogeneous fleet, and multiple visits between stations and…

Optimization and Control · Mathematics 2024-07-26 Julio-Mario Daza-Escorcia , David Álvarez Martínez

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions.…

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…

Machine Learning · Computer Science 2025-02-10 Zhihao Li , Haoze Song , Di Xiao , Zhilu Lai , Wei Wang

This paper presents a new control, namely additive-state-decomposition dynamic inversion stabilized control, that is used to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties…

Systems and Control · Computer Science 2020-03-10 Quan Quan , Guangxun Du , Kai-Yuan Cai