Search:
Match:
7 results
Research Paper#Numerical Analysis, Optimization, Uncertainty Quantification🔬 ResearchAnalyzed: Jan 3, 2026 16:59

Efficient Preconditioners for PDE-Constrained Optimization with Uncertainty

Published:Dec 29, 2025 19:03
1 min read
ArXiv

Analysis

This paper addresses the computational challenges of solving optimal control problems governed by PDEs with uncertain coefficients. The authors propose hierarchical preconditioners to accelerate iterative solvers, improving efficiency for large-scale problems arising from uncertainty quantification. The focus on both steady-state and time-dependent applications highlights the broad applicability of the method.
Reference

“The proposed preconditioners significantly accelerate the convergence of iterative solvers compared to existing methods.”

PermalinkArXiv
Paper#Numerical Analysis, Finite Element Methods, Interface Problems🔬 ResearchAnalyzed: Jan 3, 2026 16:10

Frenet-Immersed Finite Elements on Triangular Meshes for Interface Problems

Published:Dec 29, 2025 06:37
1 min read
ArXiv

Analysis

This paper introduces a novel approach to solve elliptic interface problems using geometry-conforming immersed finite element (GC-IFE) spaces on triangular meshes. The key innovation lies in the use of a Frenet-Serret mapping to simplify the interface and allow for exact imposition of jump conditions. The paper extends existing work from rectangular to triangular meshes, offering new construction methods and demonstrating optimal approximation capabilities. This is significant because it provides a more flexible and accurate method for solving problems with complex interfaces, which are common in many scientific and engineering applications.
Reference

“The paper demonstrates optimal convergence rates in the $H^1$ and $L^2$ norms when incorporating the proposed spaces into interior penalty discontinuous Galerkin methods.”

PermalinkArXiv
Research Paper#Computational Acoustics, Stochastic Methods, Domain Decomposition🔬 ResearchAnalyzed: Jan 3, 2026 16:17

Domain Decomposition for Acoustic Wave Propagation in Random Media

Published:Dec 28, 2025 18:02
1 min read
ArXiv

Analysis

This paper addresses the computationally expensive problem of simulating acoustic wave propagation in complex, random media. It leverages a sampling-free stochastic Galerkin method combined with domain decomposition techniques to improve scalability. The use of polynomial chaos expansion (PCE) and iterative solvers with preconditioners suggests an efficient approach to handle the high dimensionality and computational cost associated with the problem. The focus on scalability with increasing mesh size, time steps, and random parameters is a key aspect.
Reference

“The paper utilizes a sampling-free intrusive stochastic Galerkin approach and domain decomposition (DD)-based solvers.”

PermalinkArXiv
Research Paper#Computational Fluid Dynamics, Reduced Order Modeling, Navier-Stokes Equations🔬 ResearchAnalyzed: Jan 3, 2026 19:54

ROM for Viscous, Incompressible Flow: Exponential Convergence

Published:Dec 27, 2025 11:50
1 min read
ArXiv

Analysis

This paper investigates the use of Reduced Order Models (ROMs) for approximating solutions to the Navier-Stokes equations, specifically focusing on viscous, incompressible flow within polygonal domains. The key contribution is demonstrating exponential convergence rates for these ROM approximations, which is a significant improvement over slower convergence rates often seen in numerical simulations. This is achieved by leveraging recent results on the regularity of solutions and applying them to the analysis of Kolmogorov n-widths and POD Galerkin methods. The paper's findings suggest that ROMs can provide highly accurate and efficient solutions for this class of problems.
Reference

“The paper demonstrates "exponential convergence rates of POD Galerkin methods that are based on truth solutions which are obtained offline from low-order, divergence stable mixed Finite Element discretizations."”

PermalinkArXiv
Research#llm🔬 ResearchAnalyzed: Jan 4, 2026 10:26

MAD-NG: Meta-Auto-Decoder Neural Galerkin Method for Solving Parametric Partial Differential Equations

Published:Dec 25, 2025 11:27
1 min read
ArXiv

Analysis

This article introduces a novel method, MAD-NG, for solving parametric partial differential equations (PDEs). The method combines meta-learning and neural Galerkin methods. The focus is on the application of AI techniques to solve complex mathematical problems.
Reference

“”

PermalinkArXiv
Research#Scientific Computing🔬 ResearchAnalyzed: Jan 10, 2026 11:02

Accelerating Scientific Computing: GPU Preconditioning for Discontinuous Galerkin Methods

Published:Dec 15, 2025 18:11
1 min read
ArXiv

Analysis

This research paper explores the optimization of numerical methods, specifically Hybridizable Discontinuous Galerkin (HDG), for GPU architectures, which is crucial for high-performance scientific simulations. The focus on preconditioning techniques suggests an attempt to improve the computational efficiency and scalability of HDG discretizations on GPUs.
Reference

“The paper focuses on preconditioning techniques for Hybridizable Discontinuous Galerkin Discretizations on GPU Architectures.”

PermalinkArXiv
Research#Graphene🔬 ResearchAnalyzed: Jan 10, 2026 13:24

Advanced Simulation of Graphene Electronics Using Boltzmann Transport

Published:Dec 2, 2025 20:05
1 min read
ArXiv

Analysis

This research paper introduces a novel computational method for modeling electron transport in graphene-based devices. The discontinuous Galerkin approach allows for a more accurate and efficient simulation of complex electronic behavior.
Reference

“A discontinuous Galerkin approach for simulating graphene-based electron devices via the Boltzmann transport equation”

PermalinkArXiv