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20042026
most citedScikit-learn: Machine Learning in Python

63.6k citations

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15 papers · 1 filter

math.NA2025★ 5 cited

A coupled finite element-virtual element method for thermomechanical analysis of electronic packaging structures

Yanpeng Gong, Sishuai Li, Yue Mei +4

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computatio…

math.NA2025★ 3 cited

Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging

Yanpeng Gong, Yida He, Yue Mei +3

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditiona…

math.NA2023★ 309 cited

Phase-field modeling of fluid-driven dynamic cracking in porous media

Shuwei Zhou, Xiaoying Zhuang, Timon Rabczuk

A phase field model for fluid-driven dynamic crack propagation in poroelastic media is proposed. Therefore, classical Biot poroelasticity theory is applied in the porous medium whi…

math.NA2023★ 7 cited

Isogeometric analysis of insoluble surfactant spreading on a thin film

David Medina, Navid Valizadeh, Esteban Samaniego +2

In this paper we tackle the problem of surfactant spreading on a thin liquid film in the framework of isogeometric analysis. We consider a mathematical model that describes this ph…

math.NA2021★ 1 cited

A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation

Ritukesh Bharali, Somdatta Goswami, Cosmin Anitescu +1

The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithi…

math.NA2021★ 467 cited

A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

Hongwei Guo, Xiaoying Zhuang, Timon Rabczuk

In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms invol…

math.NA2019★ 27 cited

Isogeometric Analysis for Surface PDEs with Extended Loop Subdivision

Qing Pan, Timon Rabczuk, Gang Xu +1

We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to ea…

math.NA2019

Threshold shift method for reliability-based design optimization

Somdatta Goswami, Souvik Chakraborty, Rajib Chowdhury +1

We present a novel approach, referred to as the 'threshold shift method' (TSM), for reliability based design optimization (RBDO). The proposed approach is similar in spirit with th…

math.NA2018★ 2 cited

Isogeometric analysis with local adaptivity based on a posterior error estimation for elastodynamics

Peng Yu, Cosmin Anitescu, Satyendra Tomar +2

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on…

math.NA2017★ 3 cited

An improved isogeometric analysis method for trimmed geometries

Jinlan Xu, Ningning Sun, Laixin Shu +2

Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design(CAD). In this paper, an improved isogeometric analysis(IGA) method for trimmed geomet…

math.NA2017★ 27 cited

Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

Aishwarya Pawar, Yongjie Zhanga, Yue Jia +4

We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B…

math.NA2012★ 335 cited

NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter

Navid Valizadeh, Sundararajan Natarajan, Octavio A Gonzalez-Estrada +3

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FG…

math.NA2012★ 721 cited

Isogeometric analysis: an overview and computer implementation aspects

Vinh Phu Nguyen, Stéphane P. A. Bordas, Timon Rabczuk

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided…

math.NA2012★ 1 cited

On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures

S. Natarajan, T. Rabczuk, S. Bordas +1

In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate the…

math.NA2011★ 159 cited

Natural frequencies of cracked functionally graded material plates by the extended finite element method

S Natarajan, PM Baiz, S Bordas +2

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate…