arXiv subjects

Xiaodong Wei

Publications and source records attributed to Xiaodong Wei.

17 recordsLinked to original sources

arXiv2026

SplineNet: An Isogeometric Deep Learning Method for Complex Shells

We present a novel isogeometric deep learning method, termed SplineNet, for the seamless design and analysis of shell structures with complex geometries. The proposed approach is built upon watertight spline representations, e.g., analysis-suitable unstructured T-splines, and features exact geometric descriptions of Computer-Aided Design (CAD) models in neural networks. Bézier extraction is used to build the network architecture, where Bernstein polynomials serve as the nonlinear activation functions. SplineNet can be applied in a data-free or data-driven way. In the data-free case, energy-based formulations can be naturally incorporated as loss terms, which fulfill the need of Computer-Aided Engineering (CAE) and can be accurately calculated. In particular, the Kirchhoff--Love (KL) model is adopted to solve for the mechanical behaviors of shell structures. This way, CAD and CAE can be tightly integrated in a deep neural network without the time-consuming model/data exchange process. In the data-driven case, SplineNet can be used as the trunk net of Deep Operator Networks (DeepONet) to provide interpretability. Given such a trained network and unseen input data, results can be immediately obtained without retraining the network or repeatedly performing the traditional workflow for analysis. In the end, a variety of numerical examples are studied to demonstrate the effectiveness of the proposed method, especially when real-world complex geometries are involved.

cs.LG↗

arXiv2026

eCNNTO: A Highly Generalizable ConvNet for Accelerating Topology Optimization

This work proposes an element-based Convolutional Neural Network (CNN) to accelerate density-based Topology Optimization (TO), termed eCNNTO. TO generally undergoes a large number of iterations, where finite element analysis is performed in every iteration, leading to the efficiency bottleneck especially when dense meshes are used to achieve high-resolution designs. To address this limitation, eCNNTO is proposed to build upon Kallioras et al. (2020), where a Deep Belief Network (DBN) was trained for every element to predict its near-optimal density from its early history, thereby skipping the great majority of iterations and significantly accelerating the TO procedure. However, the method lacks spatial correlations among neighboring elements and may lead to disconnected features in the final structure. The proposed method employs CNN with residual connections to address this issue. On top of it, a novel training strategy is introduced to further enhance the optimization efficiency, where the training dataset consists of the final stage density histories rather than early ones. This change can also help reduce the required training data size. eCNNTO requires only a small dataset to train and yet it can be generalized to problems with largely different boundary conditions, loading cases, design domain geometries, mesh resolutions, as well as non-design domains. In the end, the generalization capabilities and efficiency of eCNNTO are demonstrated through a variety of examples in two and three dimensions, achieving up to 90% and 97% reduction of iterations, respectively.

cs.AI↗

arXiv2026

Weighted Quadrature on Unstructured Splines

This work presents a weighted quadrature (WQ) method to fast assemble Galerkin matrices based on unstructured spline surfaces. The method is developed upon a particular variant of unstructured splines, namely the bicubic analysis-suitable unstructured T-splines (ASUTS). While existing WQ approaches have significant speedup for structured splines (e.g., B-splines), their extension to unstructured splines faces several challenges: (1) lack of a global parametric domain for defining quadrature points, (2) a varying number of basis functions across elements that complicates the determination of the optimal number of quadrature points, and (3) ill-conditioned underdetermined linear systems that must be solved to find the quadrature weights. To solve these issues, we first define the WQ rule directly in the physical domain. Second, we specify the number of quadrature points function-wise (rather than element-wise), which naturally satisfies the well-posedness condition, namely the number of unknown weights no less than that of exactness constraints. Third, we employ the truncated Singular Value Decomposition to improve the conditioning of the underdetermined systems by discarding extremely small singular values, which are caused by the splines around extraordinary points. Several different model problems are studied, such as Poisson's problem, the biharmonic problem, and the nonlinear heat transfer problem. In the end, a variety of numerical tests are performed to demonstrate the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2026

PolyCrysDiff: Controllable Generation of Three-Dimensional Computable Polycrystalline Material Structures

The three-dimensional (3D) microstructures of polycrystalline materials exert a critical influence on their mechanical and physical properties. Realistic, controllable construction of these microstructures is a key step toward elucidating structure-property relationships, yet remains a formidable challenge. Herein, we propose PolyCrysDiff, a framework based on conditional latent diffusion that enables the end-to-end generation of computable 3D polycrystalline microstructures. Comprehensive qualitative and quantitative evaluations demonstrate that PolyCrysDiff faithfully reproduces target grain morphologies, orientation distributions, and 3D spatial correlations, while achieving an $R^2$ over 0.972 on grain attributes (e.g., size and sphericity) control, thereby outperforming mainstream approaches such as Markov random field (MRF)- and convolutional neural network (CNN)-based methods. The computability and physical validity of the generated microstructures are verified through a series of crystal plasticity finite element method (CPFEM) simulations. Leveraging PolyCrysDiff's controllable generative capability, we systematically elucidate how grain-level microstructural characteristics affect the mechanical properties of polycrystalline materials. This development is expected to pave a key step toward accelerated, data-driven optimization and design of polycrystalline materials.

cs.CV↗

arXiv2024

Scalable Field-Aligned Reparameterization for Trimmed NURBS

In engineering design, one of the most daunting problems in the design-through-analysis workflow is to deal with trimmed NURBS (Non-Uniform Rational B-Splines), which often involve topological/geometric issues and lead to inevitable gaps and overlaps in the model. Given the dominance of the trimming technology in CAD systems, reconstructing such a model as a watertight representation is highly desired. While remarkable progress has been made in recent years, especially with the advancement of isogeometric analysis (IGA), there still lack a fully automatic and scalable tool to achieve this reconstruction goal. To address this issue, we present a semi-automatic and scalable reparameterization pipeline based on a scalable and feature-aligned meshing tool, QuadriFlow [1]. On top of it, we provide support for open surfaces to deal with engineering shell structures, and perform sophisticated patch simplification to remove undesired tiny/slender patches. As a result, we obtain a watertight spline surface (multi-patch NURBS or unstructured splines) with a simple quadrilateral layout. Through several challenging models from industry applications, we demonstrate the efficacy and efficiency of the proposed pipeline as well as its integration with IGA. Our source code is publicly available on GitHub [2].

cs.CG↗

arXiv2023

Stabilized isogeometric formulation of the Stokes problem on overlapping patches

We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but predefined hierarchical order. All the visible regions constitute the computational domain, whereas independent patches are coupled through visible interfaces using Nitsche's formulation. Such a geometric representation inevitably involves trimming, which may yield trimmed elements of extremely small measures (referred to as bad elements) and thus lead to the instability issue. Motivated by the minimal stabilization method that rigorously guarantees stability for trimmed geometries [1], in this work we generalize it to the Stokes problem on overlapping patches. Central to our method is the distinct treatments for the pressure and velocity spaces: Stabilization for velocity is carried out for the flux terms on interfaces, whereas pressure is stabilized in all the bad elements. We provide a priori error estimates with a comprehensive theoretical study. Through a suite of numerical tests, we first show that optimal convergence rates are achieved, which consistently agrees with our theoretical findings. Second, we show that the accuracy of pressure is significantly improved by several orders using the proposed stabilization method, compared to the results without stabilization. Finally, we also demonstrate the flexibility and efficiency of the proposed method in capturing local features in the solution field.

math.NA↗

arXiv2023

Kirchhoff-Love shell representation and analysis using triangle configuration B-splines

This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation requires global $C^1$-continuous basis functions. The nonuniform rational B-spline (NURBS)-based IGA has been extensively used for developing Kirchhoff-Love shell elements. However, shells with complex geometries inevitably need multiple patches and trimming techniques, where stitching patches with high continuity is a challenge. On the other hand, due to their unstructured nature, TCB-splines can accommodate general polygonal domains, have local refinement, and are flexible to model complex geometries with $C^1$ continuity, which naturally fit into the Kirchhoff-Love shell formulation with complex geometries. Therefore, we propose to use TCB-splines as basis functions for geometric representation and solution approximation. We apply our method to both linear and nonlinear benchmark shell problems, where the accuracy and robustness are validated. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff-Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines.

cs.CE↗

arXiv2023

Isogeometric analysis using G-spline surfaces with arbitrary unstructured quadrilateral layout

G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the Bubnov-Galerkin method to solve partial differential equations with G-splines results in discretizations with global C^1 continuity in physical space. Extraordinary points (EPs) are required to represent manifold surfaces with arbitrary topological genus. In this work, we allow both interior and boundary EPs and there are no limitations regarding how close EPs can be from each other. Reaching this level of flexibility is necessary so that splines with EPs can become mainstream in the design-through-analysis cycle of complex thin-walled structures. To the authors' knowledge, the two EP constructions based on imposing G^1 constraints proposed in this work are the first two EP constructions used in isogeometric analysis (IGA) that combine the following distinctive characteristics: (1) Only vertex-based control points are used and they behave as geometric shape handles, (2) any control point of the control net can potentially be an EP, (3) global C^1 continuity in physical space is obtained without introducing singularities, (4) faces around EPs are not split into multiple elements, and (5) good surface quality is attained. The studies of convergence and surface quality performed in this paper suggest that G-splines are more suitable for IGA than EP constructions based on the D-patch framework. Finally, we have represented the stiffener, the inner part, and the outer part of a B-pillar with G-spline surfaces and solved eigenvalue problems using both Kirchhoff-Love and Reissner-Mindlin shell theories. The results are compared with bilinear quadrilateral meshes and excellent agreement is found between G-splines and conventional finite elements.

cs.CE↗

arXiv2021

Robust Numerical Integration on Curved Polyhedra Based on Folded Decompositions

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the given parametric surfaces. Each pyramid serves as an integration cell with a geometric mapping from a standard parent domain (e.g., a unit cube), where the tensor-product Gauss quadrature is adopted. As no constraint is imposed on the decomposition, certain resulting pyramids may intersect with themselves, and thus their geometric mappings may present negative Jacobian values. We call such cells the folded cells and refer to the corresponding decomposition as a folded decomposition. We show that folded cells do not cause any issues in practice as they are only used to numerically compute certain integrals of interest. The same idea can be applied to planar curved polygons as well. We demonstrate both theoretically and numerically that folded cells can retain the same accuracy as the cells with strictly positive Jacobians. On the other hand, folded cells allow for a much easier and much more flexible decomposition for general curved polyhedra, on which one can robustly compute integrals. In the end, we show that folded cells can flexibly and robustly accommodate real-world complex geometries by presenting several examples in the context of immersed isogeometric analysis, where involved sharp features can be well respected in generating integration cells.

math.NA↗

arXiv2021

Immersed Boundary-Conformal Isogeometric Method for Linear Elliptic Problems

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche's method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method [1]. In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

math.NA↗

arXiv2021

THU-Splines: Highly Localized Refinement on Smooth Unstructured Splines

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local $h$-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is taken as the input control mesh, where the degenerated-patch method [18] is adopted in irregular regions to define $C^1$-continuous bicubic splines, whereas regular regions only involve $C^2$ B-splines. Irregular regions are then smoothly joined with regular regions through the truncation mechanism [29], leading to a globally smooth spline construction. Subsequently, local refinement is performed following the truncated hierarchical B-spline construction [10] to achieve a flexible refinement without propagating to unanticipated regions. Challenges lie in refining transition regions where a mixed types of splines play a role. THU-spline basis functions are globally $C^1$-continuous and are non-negative everywhere except near extraordinary vertices, where slight negativity is inevitable to retain refinability of the spline functions defined using the degenerated-patch method. Such functions also have a finite representation that can be easily integrated with existing finite element or isogeometric codes through Bézier extraction.

math.NA↗

arXiv2021

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow multiple extraordinary points within the same face. This generalization drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be generated to represent a certain geometry. The AST-spline spaces detailed in this work have $C^1$ inter-element continuity near extraordinary points and $C^2$ inter-element continuity elsewhere. We mathematically show that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. We numerically show that AST-splines with multiple extraordinary points per face lead to optimal convergence rates for second- and fourth-order linear elliptic problems. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bézier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements. Good agreement is found, but conventional finite elements require significantly more degrees of freedom to reach a converged solution than AST-splines.

math.NA↗

arXiv2020

HexGen and Hex2Spline: Polycube-based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA

In this paper, we present two software packages, HexGen and Hex2Spline, that seamlessly integrate geometry design with isogeometric analysis (IGA) in LS-DYNA. Given a boundary representation of a solid model, HexGen creates a hexahedral mesh by utilizing a semi-automatic polycube-based mesh generation method. Hex2Spline takes the output hexahedral mesh from HexGen as the input control mesh and constructs volumetric truncated hierarchical splines. Through Bézier extraction, Hex2Spline transfers spline information to LS-DYNA and performs IGA therein. We explain the underlying algorithms in each software package and use a rod model to explain how to run the software. We also apply our software to several other complex models to test its robustness. Our goal is to provide a robust volumetric modeling tool and thus expand the boundary of IGA to volume-based industrial applications.

cs.CG↗

arXiv2020

Small-Footprint Keyword Spotting with Multi-Scale Temporal Convolution

Keyword Spotting (KWS) plays a vital role in human-computer interaction for smart on-device terminals and service robots. It remains challenging to achieve the trade-off between small footprint and high accuracy for KWS task. In this paper, we explore the application of multi-scale temporal modeling to the small-footprint keyword spotting task. We propose a multi-branch temporal convolution module (MTConv), a CNN block consisting of multiple temporal convolution filters with different kernel sizes, which enriches temporal feature space. Besides, taking advantage of temporal and depthwise convolution, a temporal efficient neural network (TENet) is designed for KWS system. Based on the purposed model, we replace standard temporal convolution layers with MTConvs that can be trained for better performance. While at the inference stage, the MTConv can be equivalently converted to the base convolution architecture, so that no extra parameters and computational costs are added compared to the base model. The results on Google Speech Command Dataset show that one of our models trained with MTConv performs the accuracy of 96.8% with only 100K parameters.

eess.AS↗

arXiv2020

Tuned Hybrid Non-Uniform Subdivision Surfaces with Optimal Convergence Rates

This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $λ$ ($\frac{1}{4}<λ<1$) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid non-uniform subdivision (tHNUS). Our previous work corresponds to the case when $λ=\frac{1}{2}$. While introducing $λ$ in hybrid subdivision significantly complicates the theoretical proof of $G^1$ continuity around extraordinary vertices, reducing $λ$ can recover the optimal convergence rates when tuned hybrid subdivision functions are used as a basis in isogeometric analysis. From the geometric point of view, the tHNUS retains comparable shape quality as [19] under non-uniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tuned hybrid subdivision surface is globally $G^1$-continuous. From the analysis point of view, tHNUS basis functions form a non-negative partition of unity, are globally linearly independent, and their spline spaces are nested. We numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with non-uniform parameterization around extraordinary vertices.

math.NA↗

arXiv2019

Overlapping Multi-Patch Isogeometric Method with Minimal Stabilization

We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union and intersection. Particularly, this work focuses on the union operation, which involves multiple independent, generally non-conforming and trimmed spline patches. Given a series of patches, we overlay one on top of another in a certain order. While the invisible part of each patch is trimmed away, the visible parts of all the patches constitute the entire computational domain. We employ the Nitsche's method to weakly couple independent patches through visible interfaces. Moreover, we propose a minimal stabilization method to address the instability issue that arises on the interfaces shared by small trimmed elements. We show in theory that our proposed method recovers stability and guarantees well-posedness of the problem as well as optimal error estimates. In the end, we numerically verify the theory by solving the Poisson's equation on various geometries that are obtained by the union operation.

math.NA↗

arXiv2017

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

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-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

math.NA↗