The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully disc...The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.展开更多
.In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under....In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under the assumption that the double saddle-point problem exists a unique solution.An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain(DLM/FD)finite element method for solving elliptic interface problems is also presented,in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method.Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.展开更多
Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite vol...Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC[49,50].By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach,we efficiently achieve a fast convergence and reasonable solutions for this multiphase,multiphysics PEMFC model.Numerical implementation is done by using a novel automated finite element/finite volume programgenerator(FEPG).By virtue of a high-level algorithmdescription language(script),component programming and human intelligence technologies,FEPG can quickly generate finite element/finite volume source code for PEMFC simulation.Thus,one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods.Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D,multiphysics PEMFC model with multicomponent and multiphase mechanism.展开更多
In this paper,we apply streamline-diffusion and Galerkin-least-squares fi-nite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell(PEFC)that contains a gas channel and a...In this paper,we apply streamline-diffusion and Galerkin-least-squares fi-nite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell(PEFC)that contains a gas channel and a gas diffusion layer(GDL).This two-phase PEFC model is typically modeled by a modified Navier-Stokes equation for the mass and momentum,with Darcy’s drag as an additional source term in momentum for flows through GDL,and a discontinuous and degenerate convectiondiffusion equation for water concentration.Based on the mixed finite element method for the modified Navier-Stokes equation and standard finite element method for water equation,we design streamline-diffusion and Galerkin-least-squares to overcome the dominant convection arising from the gas channel.Meanwhile,we employ Kirchhoff transformation to deal with the discontinuous and degenerate diffusivity in water concentration.Numerical experiments demonstrate that our finite element methods,together with these numerical techniques,are able to get accurate physical solutions with fast convergence.展开更多
Blood pressure(BP)has been identified as one of the main factors in cardiovascular disease and other related diseases.Then how to accurately and conveniently measure BP is important to monitor BP and to prevent hypert...Blood pressure(BP)has been identified as one of the main factors in cardiovascular disease and other related diseases.Then how to accurately and conveniently measure BP is important to monitor BP and to prevent hypertension.This paper proposes an efficient BP measurement model by integrating a fluid-structure interaction model with the photoplethysmogram(PPG)signal and developing a data-driven computational approach to fit two optimization parameters in the proposedmodel for each individual.The developed BPmodel has been validated on a public BP dataset and has shown that the average prediction errors among the root mean square error(RMSE),the mean absolute error(MAE),the systolic blood pressure(SBP)error,and the diastolic blood pressure(DBP)error are all below 5mmHg for normal BP,stage I,and stage II hypertension groups,and,prediction accuracies of the SBP and the DBP are around 96%among those three groups.展开更多
In this paper,we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface.We employ an energetic variational phase field model to desc...In this paper,we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface.We employ an energetic variational phase field model to describe its physical phenomena,and obtain the corresponding governing equations defined by a modi-fied Navier-Stokes equations coupled with phase field and energy transport.A mixed Taylor-Hood finite element discretization together with full Newton’s method are applied to this strongly nonlinear phase field model on a specific domain.Under different boundary conditions of temperature,the resulting numerical solutions illustrate that the thermal energy plays a fundamental role in the interfacial dynamics of two-phase flows.In particular,it gives rise to a dynamic interfacial tension that depends on the direction of temperature gradient,determining the movement of the interface along a sine/cosine-like curve.展开更多
基金P.Sun was supported by NSF Grant DMS-1418806C.S.Zhang was partially supported by the National Key Research and Development Program of China(Grant No.2016YFB0201304)+1 种基金the Major Research Plan of National Natural Science Foundation of China(Grant Nos.91430215,91530323)the Key Research Program of Frontier Sciences of CAS.
文摘The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.
基金supported by the 10 plus 10 project of Tongji University(No.4260141304/004/010).
文摘.In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under the assumption that the double saddle-point problem exists a unique solution.An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain(DLM/FD)finite element method for solving elliptic interface problems is also presented,in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method.Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.
基金supported by NSF Grant DMS-0913757 and 111-Program for energysaving and environment-friendly automobile(B08019)of ChinaPengtao Sun was also partially supported by State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences during his visit in July,2010.Su Zhou is supported by 863 Program(2008AA050403)+2 种基金Shanghai Pujiang Talent Plan(08PJ1409)of China.Qiya Hu is supported by The Key Project of Natural Science Foundation of China G11031006National Basic Research Programof China G2011309702Natural Science Foundation of China G10771178.
文摘Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this paper.Due to the coexistence of multiphase regions,the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC[49,50].By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach,we efficiently achieve a fast convergence and reasonable solutions for this multiphase,multiphysics PEMFC model.Numerical implementation is done by using a novel automated finite element/finite volume programgenerator(FEPG).By virtue of a high-level algorithmdescription language(script),component programming and human intelligence technologies,FEPG can quickly generate finite element/finite volume source code for PEMFC simulation.Thus,one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods.Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D,multiphysics PEMFC model with multicomponent and multiphase mechanism.
基金This work was supported in part by NSF DMS-0609727,the Center for Computa-tional Mathematics and Applications of Penn State University.J.Xu was also supported in part by NSFC-10501001 and Alexander H.Humboldt Foundation.
文摘In this paper,we apply streamline-diffusion and Galerkin-least-squares fi-nite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell(PEFC)that contains a gas channel and a gas diffusion layer(GDL).This two-phase PEFC model is typically modeled by a modified Navier-Stokes equation for the mass and momentum,with Darcy’s drag as an additional source term in momentum for flows through GDL,and a discontinuous and degenerate convectiondiffusion equation for water concentration.Based on the mixed finite element method for the modified Navier-Stokes equation and standard finite element method for water equation,we design streamline-diffusion and Galerkin-least-squares to overcome the dominant convection arising from the gas channel.Meanwhile,we employ Kirchhoff transformation to deal with the discontinuous and degenerate diffusivity in water concentration.Numerical experiments demonstrate that our finite element methods,together with these numerical techniques,are able to get accurate physical solutions with fast convergence.
基金W.Hao was supported in part by AHA grant 17SDG33660722P.Sun was supported by a grant from the Simons Foundation(MPS-706640,PS).
文摘Blood pressure(BP)has been identified as one of the main factors in cardiovascular disease and other related diseases.Then how to accurately and conveniently measure BP is important to monitor BP and to prevent hypertension.This paper proposes an efficient BP measurement model by integrating a fluid-structure interaction model with the photoplethysmogram(PPG)signal and developing a data-driven computational approach to fit two optimization parameters in the proposedmodel for each individual.The developed BPmodel has been validated on a public BP dataset and has shown that the average prediction errors among the root mean square error(RMSE),the mean absolute error(MAE),the systolic blood pressure(SBP)error,and the diastolic blood pressure(DBP)error are all below 5mmHg for normal BP,stage I,and stage II hypertension groups,and,prediction accuracies of the SBP and the DBP are around 96%among those three groups.
基金Pengtao Sun was supported in part by Research Development Award of University of Nevada Las Vegas 2220-320-980CChun Liu was supported in part by National Science Foundation Grant DMS-0707594+1 种基金Jinchao Xu was supported in part by National Science Foundation Grant DMS-0609727 and Alexander H.Humboldt FoundationThis work was also supported by the Center for Computational Mathematics and Applications of Penn State.
文摘In this paper,we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface.We employ an energetic variational phase field model to describe its physical phenomena,and obtain the corresponding governing equations defined by a modi-fied Navier-Stokes equations coupled with phase field and energy transport.A mixed Taylor-Hood finite element discretization together with full Newton’s method are applied to this strongly nonlinear phase field model on a specific domain.Under different boundary conditions of temperature,the resulting numerical solutions illustrate that the thermal energy plays a fundamental role in the interfacial dynamics of two-phase flows.In particular,it gives rise to a dynamic interfacial tension that depends on the direction of temperature gradient,determining the movement of the interface along a sine/cosine-like curve.