This paper considers the well-posedness of a special partial differential equation, whose right term is independent on the solution. With Fourier analysis, we introduce an executive procedure to analyze its well-posed...
This paper considers the well-posedness of a special partial differential equation, whose right term is independent on the solution. With Fourier analysis, we introduce an executive procedure to analyze its well-posedness by variable transformations and present some conditions under which the system is well-posed.
Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the f...
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ISBN:
(纸本)9783950353709
Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape, which can be recast in a common PDE-constrained optimization formulation.
In this paper, we investigate the model of three-dimensional (3D) stochastic multi-symplectic Hamiltonian Maxwell's equations, and consider the stochastic multi-symplectic numerical methods of solving such equatio...
In this paper, we investigate the model of three-dimensional (3D) stochastic multi-symplectic Hamiltonian Maxwell's equations, and consider the stochastic multi-symplectic numerical methods of solving such equations. In particular, multi-symplectic wavelet collocation method (MSWCM) is applied to such equations. It is shown that this multi-symplectic numerical method preserves not only the multi-symplectic structure, but also discrete energy conservation law under perfectly electric conducting boundary conditions.
Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this *** to the coexistence of multiphase regions,the standard finite element/finite volume me...
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Numerical methods of a 3D multiphysics,two-phase transport model of proton exchange membrane fuel cell(PEMFC)is studied in this *** 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 *** 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 ***,one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume *** 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.
作者：
Pingbing MingLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of Sciences
In this talk,I will touch two issues of multiscale coupling methods for *** is the so-called ghost force problem,in particular,I will explain its influence for dynamical *** issue is a simple trick to remove the ghost...
In this talk,I will touch two issues of multiscale coupling methods for *** is the so-called ghost force problem,in particular,I will explain its influence for dynamical *** issue is a simple trick to remove the ghost force,and we study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity *** show the proposed scheme converges to the solution of the atomistic model with second order *** numerical examples will also be reported.
作者：
Yana DiLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of Sciences
The talk will study the evolution of an ellipsoid particle in an incompressible,Newtonian shear flow by considering the fluid slipping at solid surface.A continuum hydrodynamic model is constructed,using phase-field d...
The talk will study the evolution of an ellipsoid particle in an incompressible,Newtonian shear flow by considering the fluid slipping at solid surface.A continuum hydrodynamic model is constructed,using phase-field diffuse-interface modeling for fluid-solid *** slipping at solid particle surface is incorporated into the model by a decrease in the shear viscosity in the interfacial *** simulations will be given to show the effect of the fluid slipping on the orientational motion of the ellipsoid particle.
This paper considers the solvability of the central box scheme to a kind of nonlinear partial differential equations by using the contraction mapping theorem in operator theory. The scales of step-sizes for the solvab...
This paper considers the solvability of the central box scheme to a kind of nonlinear partial differential equations by using the contraction mapping theorem in operator theory. The scales of step-sizes for the solvability of this scheme are derived. The result shows that the smaller the step-sizes are, the larger the radius of a region in which a stable solution exists uniquely will be.
In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible *** tension is introduced as an augmented variable to satisfy the constraint of interfac...
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In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible *** tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES *** this work,the arclength of the interface is locally and globally conserved as the enclosed region undergoes *** forces at the interface are calculated from the configuration of the interface and the computed augmented variable,and then applied to the fluid through the related jump *** governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type *** proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear *** results reveal that both the area enclosed by interface and arclength of interface are conserved well *** provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.
This paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of H1(Ω) and H2(Ω) defined on the boundary or interface of an unstructured grid. We transf...
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We treat a surface finite element method that is based on the trace of a standard finite element space on a tetrahedral triangulation of an outer domain that contains a stationary 2D surface. This surface FEM is used ...
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ISBN:
(纸本)9783950353709
We treat a surface finite element method that is based on the trace of a standard finite element space on a tetrahedral triangulation of an outer domain that contains a stationary 2D surface. This surface FEM is used to discretize partial differential equation on the surface. We demonstrate the performance of this method for stationary and time-dependent diffusion equations. For the stationary case, results of an adaptive method based on a surface residual-type error indicator are presented. Furthermore, for the advection-dominated case a SUPG stabilization is introduced. The topic of finite element stabilization for advection-dominated surface transport equations has not been addressed in the literature so far.
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