A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and nu...Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and numerical value σ relation theorem, outer P(ρ,σ)-set's range;studied other characteristics of outer P(ρ,σ)-set: give the finiteness theorem of outer P(ρ,σ)-set, the set chain theorem of outer P(ρ,σ)-set, the outer P(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P(ρ,σ)-set, filter generation theorem of outer P(ρ,σ)-set; finally give its application.展开更多
In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estima...In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.展开更多
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
基金Foundation item： Supported by the Basic and Frontier Technology Research Projects of Henan Province （132300410289） Supported by the Natural Science Foundation of Fujian Province（2012D112）
文摘Based on the conception of P(ρ,σ)-set(XP ˉFρ, XPFσ), this paper studied the relation between outer P(ρ,σ)-set and outer P-set: give outer P(ρ,σ)-set and outer P-set relation theorem, outer P(ρ,σ)-set and numerical value σ relation theorem, outer P(ρ,σ)-set's range;studied other characteristics of outer P(ρ,σ)-set: give the finiteness theorem of outer P(ρ,σ)-set, the set chain theorem of outer P(ρ,σ)-set, the outer P(ρ,σ)-set probability interval finite partition theorem, and its corollary; also give generation, reduction, identification theorem of outer P(ρ,σ)-set, filter generation theorem of outer P(ρ,σ)-set; finally give its application.
文摘In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.
