相关论文: SoftIGA: soft isogeometric analysis
In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is…
In this paper, we present the isogeometric least-squares collocation (IGA-L) method, which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense. The…
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the…
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…
The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…
We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has been applied successfully in various problems in solid mechanics, in image-based analysis, fluid-structure interaction and in many other applications. A challenging…
In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with…
We propose a new family of high-order explicit generalized-$\alpha$ methods for hyperbolic problems with the feature of dissipation control. Our approach delivers $2k,\, \left(k \in \mathbb{N}\right)$ accuracy order in time by solving $k$…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis…
An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement…
Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights.…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…