An hp version of interface penalty finite element method(hp-IPFEM)is proposed to solve the elliptic interface problems in two and three dimensions on unfitted meshes.Error estimates in broken H1 norm,which are optimal...An hp version of interface penalty finite element method(hp-IPFEM)is proposed to solve the elliptic interface problems in two and three dimensions on unfitted meshes.Error estimates in broken H1 norm,which are optimal with respect to h and suboptimal with respect to p by half an order of p,are derived.Both symmetric and non-symmetric IPFEM are considered.Error estimates in L^2 norm are proved by the duality argument.All the estimates are independent of the location of the interface relative to the meshes.Numerical examples are provided to illustrate the performance of the method.This paper is adapted from the work originally post on arXiv.com by the same authors(arXiv:1007.2893v1).展开更多
This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions.To capture discontinuities of the solution caused by interfaces,we reformulate the prob...This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions.To capture discontinuities of the solution caused by interfaces,we reformulate the problem as an energy minimization problem involving two weakly coupled components.This enables us to train two deep neural networks to represent two components of the solution in highdimensional space.The curse of dimensionality is alleviated by using theMonte-Carlo method to discretize the unfittedNitsche energy functional.We present several numerical examples to show the performance of the proposed method.展开更多
The mechanism of runs propagation of plain weft-knit-ted fabric is analyzed theoretically.The relevant physicalmodel,the mathematical equation and the new methodto test the run force are presented accordingly,and them...The mechanism of runs propagation of plain weft-knit-ted fabric is analyzed theoretically.The relevant physicalmodel,the mathematical equation and the new methodto test the run force are presented accordingly,and themeasured results are described also.The run theory hasbeen proved correct in practice,a means to improve runresist of knit is also recommended.展开更多
文摘An hp version of interface penalty finite element method(hp-IPFEM)is proposed to solve the elliptic interface problems in two and three dimensions on unfitted meshes.Error estimates in broken H1 norm,which are optimal with respect to h and suboptimal with respect to p by half an order of p,are derived.Both symmetric and non-symmetric IPFEM are considered.Error estimates in L^2 norm are proved by the duality argument.All the estimates are independent of the location of the interface relative to the meshes.Numerical examples are provided to illustrate the performance of the method.This paper is adapted from the work originally post on arXiv.com by the same authors(arXiv:1007.2893v1).
基金supported by Andrew Sisson Fund of the University of MelbourneX.Y.was partially supported by the NSF grants DMS-1818592 and DMS-2109116.
文摘This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions.To capture discontinuities of the solution caused by interfaces,we reformulate the problem as an energy minimization problem involving two weakly coupled components.This enables us to train two deep neural networks to represent two components of the solution in highdimensional space.The curse of dimensionality is alleviated by using theMonte-Carlo method to discretize the unfittedNitsche energy functional.We present several numerical examples to show the performance of the proposed method.
文摘The mechanism of runs propagation of plain weft-knit-ted fabric is analyzed theoretically.The relevant physicalmodel,the mathematical equation and the new methodto test the run force are presented accordingly,and themeasured results are described also.The run theory hasbeen proved correct in practice,a means to improve runresist of knit is also recommended.
