The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models...The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.展开更多
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc...The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.展开更多
We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uni...We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uniform gap method(UGM),highlights the critical importance of the averaged sp level density.The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical nature.Two effects generally ignored in similar fits are addressed:(a)a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions,as discussed by Möller and Nix[Nucl.Phys.A 476,1(1992)],and(b)a correction for a systematic spurious enhancement of for protons in the vicinity ofλ,caused by the local Slater approximation commonly employed in treating Coulomb exchange terms(e.g.,[Phys.Rev.C 84,014310(2011)]).This approach has demonstrated significant efficiency when applied to Hartree-Fock+Bardeen-Cooper-Schrieffer(BCS)calculations(including the seniority force and self-consistent blocking for odd nuclei)of a large sample of well and rigidly deformed even-even rare-earth nuclei.The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data[Phys.Rev.C 99,064306(2019)].In this study,we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same region.The agreement with experimental data was found to be comparable to that obtained through direct fitting,as reported in[Phys.Rev.C 99,064306(2019)].展开更多
基金the National Natural Science Foundation of China(https://www.nsfc.gov.cn/,Project No.11972179)the Natural Science Foundation of Guangdong Province(http://gdstc.gd.gov.cn/,No.2020A1515010685)the Department of Education of Guangdong Province(http://edu.gd.gov.cn/,No.2020ZDZX2008).
文摘The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.
基金supported by the National Natural Science Foundation of China(Nos.10801042 and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20104410120001)
文摘The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
基金support by the Hue University under the Core Research Program,(NCM.DHH.2018.09)Universiti Teknologi Malaysia for its UTMShine grant(Q.J130000.2454.09G96)。
文摘We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uniform gap method(UGM),highlights the critical importance of the averaged sp level density.The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical nature.Two effects generally ignored in similar fits are addressed:(a)a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions,as discussed by Möller and Nix[Nucl.Phys.A 476,1(1992)],and(b)a correction for a systematic spurious enhancement of for protons in the vicinity ofλ,caused by the local Slater approximation commonly employed in treating Coulomb exchange terms(e.g.,[Phys.Rev.C 84,014310(2011)]).This approach has demonstrated significant efficiency when applied to Hartree-Fock+Bardeen-Cooper-Schrieffer(BCS)calculations(including the seniority force and self-consistent blocking for odd nuclei)of a large sample of well and rigidly deformed even-even rare-earth nuclei.The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data[Phys.Rev.C 99,064306(2019)].In this study,we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same region.The agreement with experimental data was found to be comparable to that obtained through direct fitting,as reported in[Phys.Rev.C 99,064306(2019)].
