149 research outputs found
A fourth-order unfitted characteristic finite element method for solving the advection-diffusion equation on time-varying domains
We propose a fourth-order unfitted characteristic finite element method to
solve the advection-diffusion equation on time-varying domains. Based on a
characteristic-Galerkin formulation, our method combines the cubic MARS method
for interface tracking, the fourth-order backward differentiation formula for
temporal integration, and an unfitted finite element method for spatial
discretization. Our convergence analysis includes errors of discretely
representing the moving boundary, tracing boundary markers, and the spatial
discretization and the temporal integration of the governing equation.
Numerical experiments are performed on a rotating domain and a severely
deformed domain to verify our theoretical results and to demonstrate the
optimal convergence of the proposed method
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
A robust topology optimization (RTO) approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach
Tensor-based Intrinsic Subspace Representation Learning for Multi-view Clustering
As a hot research topic, many multi-view clustering approaches are proposed
over the past few years. Nevertheless, most existing algorithms merely take the
consensus information among different views into consideration for clustering.
Actually, it may hinder the multi-view clustering performance in real-life
applications, since different views usually contain diverse statistic
properties. To address this problem, we propose a novel Tensor-based Intrinsic
Subspace Representation Learning (TISRL) for multi-view clustering in this
paper. Concretely, the rank preserving decomposition is proposed firstly to
effectively deal with the diverse statistic information contained in different
views. Then, to achieve the intrinsic subspace representation, the
tensor-singular value decomposition based low-rank tensor constraint is also
utilized in our method. It can be seen that specific information contained in
different views is fully investigated by the rank preserving decomposition, and
the high-order correlations of multi-view data are also mined by the low-rank
tensor constraint. The objective function can be optimized by an augmented
Lagrangian multiplier based alternating direction minimization algorithm.
Experimental results on nine common used real-world multi-view datasets
illustrate the superiority of TISRL
Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design
A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency
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