Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present...Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative.Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.展开更多
We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is...We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.展开更多
We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued images.Based on the primal-dual formulation of the original nondifferentiable model,t...We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued images.Based on the primal-dual formulation of the original nondifferentiable model,the new algorithm updates the primal and dual variables alternately using the gradient descent/ascent flows.Numerical examples are provided to demonstrate the superiority of our algorithm.展开更多
In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,...In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,the two tangent components of the displacement are discretized by using conformingfinite elements(linear element),and the normal component of the displacement is discretized by us-ing conforming Hsieh-Clough-Tocher element(HCT element).Then,the existence,uniqueness,stability,convergence and a priori error estimate of the corresponding analyses are proven and analyzed.Finally,we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.展开更多
基金supported in part by the National Key Basic Research Program under grant 2022YFA1004402the Science and Technology Commission of Shanghai Municipality(Nos.21JC1402500,22ZR1421900,and 22DZ2229014)the National Natural Science Foundation of China under grant(No.12071149).
文摘Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative.Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.
基金This work was supported in part by the National Natural Science Foundation of China under grants(No.11571115 and No.12071149)Natural Science Foundation of Shanghai(No.19ZR1414100)Science and Technology Commission of Shanghai Municipality(No.18dz2271000).
文摘We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.
文摘We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued images.Based on the primal-dual formulation of the original nondifferentiable model,the new algorithm updates the primal and dual variables alternately using the gradient descent/ascent flows.Numerical examples are provided to demonstrate the superiority of our algorithm.
基金supported by the National Natural Science Foundation of China(NSFC Nos.11971379,12071149)the Natural Science Foundation of Shanghai(Grant No.19ZR1414100)。
文摘In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,the two tangent components of the displacement are discretized by using conformingfinite elements(linear element),and the normal component of the displacement is discretized by us-ing conforming Hsieh-Clough-Tocher element(HCT element).Then,the existence,uniqueness,stability,convergence and a priori error estimate of the corresponding analyses are proven and analyzed.Finally,we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.
