Text only print
Full screen print
Numerical Analysis Seminar
Seminar information archive ～12/31｜Next seminar｜Future seminars 01/01～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
Seminar information archive
2016/05/09
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ken'ichiro Tanaka (Musashino University)
Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces
(日本語)
Ken'ichiro Tanaka (Musashino University)
Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces
(日本語)
2016/04/18
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takahito Kashiwabara (University of Tokyo)
Error estimate for the finite element method in a smooth domain (日本語)
Takahito Kashiwabara (University of Tokyo)
Error estimate for the finite element method in a smooth domain (日本語)
2016/04/04
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Eric Chung (Chinese University of Hong Kong)
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)
Eric Chung (Chinese University of Hong Kong)
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)
[ Abstract ]
In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.
In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.
2015/10/26
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Fredrik Lindgren (Osaka University)
Numerical approximation of spinodal decomposition in the presence of noise (English)
Fredrik Lindgren (Osaka University)
Numerical approximation of spinodal decomposition in the presence of noise (English)
[ Abstract ]
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.
In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.
We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.
If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.
This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.
In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.
We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.
If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.
This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).
2015/06/29
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshio Komori (Kyushu Institute of Technology)
Stabilized Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations (日本語)
Yoshio Komori (Kyushu Institute of Technology)
Stabilized Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations (日本語)
[ Abstract ]
We are concerned with numerical methods which give weak approximations for stiff It\^{o} stochastic differential equations (SDEs). Implicit methods are one of good candidates to deal with such SDEs. In fact, a well-designed implicit method has been recently proposed by Abdulle and his colleagues [Abdulle et al. 2013a]. On the other hand, it is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods [Abdulle et al. 2013b]. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods [Hochbruck et al. 2005, 2010] when applied to semilinear ODEs.
In this talk, we will propose new exponential RK methods which achieve weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term. We will analytically investigate their stability properties in mean square, and will check their performance in numerical experiments.
(This is a joint work with D. Cohen and K. Burrage.)
We are concerned with numerical methods which give weak approximations for stiff It\^{o} stochastic differential equations (SDEs). Implicit methods are one of good candidates to deal with such SDEs. In fact, a well-designed implicit method has been recently proposed by Abdulle and his colleagues [Abdulle et al. 2013a]. On the other hand, it is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods [Abdulle et al. 2013b]. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods [Hochbruck et al. 2005, 2010] when applied to semilinear ODEs.
In this talk, we will propose new exponential RK methods which achieve weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term. We will analytically investigate their stability properties in mean square, and will check their performance in numerical experiments.
(This is a joint work with D. Cohen and K. Burrage.)
2015/06/15
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuto Miyatake (Nagoya University)
Parallel energy-preserving methods for Hamiltonian systems (日本語)
Yuto Miyatake (Nagoya University)
Parallel energy-preserving methods for Hamiltonian systems (日本語)
2015/05/18
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Katsuhisa Ozaki (Shibaura Institute of Technology)
Accurate matrix multiplication by error-free transformation (日本語)
Katsuhisa Ozaki (Shibaura Institute of Technology)
Accurate matrix multiplication by error-free transformation (日本語)
2015/04/27
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Akitoshi Takayasu (Waseda University)
A method of verified computations for solutions to semilinear parabolic equations using an analytic semigroup (日本語)
Akitoshi Takayasu (Waseda University)
A method of verified computations for solutions to semilinear parabolic equations using an analytic semigroup (日本語)
2015/03/20
13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Gadi Fibich (Tel Aviv University)
Asymmetric Auctions (English)
Gadi Fibich (Tel Aviv University)
Asymmetric Auctions (English)
[ Abstract ]
Auctions are central to the modern economy, both on-line and off-line. A fundamental result in auction theory is that when bidders are symmetric (identical), then under quite general conditions, all auctions are revenue equivalent. While it is known that this result does not hold when bidders are asymmetric, the effect of bidders' asymmetry is poorly understood, since asymmetric auctions are much harder to analyze.
In this talk I will discuss the mathematical theory of asymmetric auctions. I will focus on asymmetric first-price auctions, where the mathematical model is given by a nonstandard system of $n$ nonlinear ordinary differential equations, with $2n$ boundary conditions and a free boundary. I will present various analytic and numerical approaches for this system. Then I will present some recent results on asymptotic revenue equivalence of asymmetric auctions.
Joint work with A. Gavious and N. Gavish.
Auctions are central to the modern economy, both on-line and off-line. A fundamental result in auction theory is that when bidders are symmetric (identical), then under quite general conditions, all auctions are revenue equivalent. While it is known that this result does not hold when bidders are asymmetric, the effect of bidders' asymmetry is poorly understood, since asymmetric auctions are much harder to analyze.
In this talk I will discuss the mathematical theory of asymmetric auctions. I will focus on asymmetric first-price auctions, where the mathematical model is given by a nonstandard system of $n$ nonlinear ordinary differential equations, with $2n$ boundary conditions and a free boundary. I will present various analytic and numerical approaches for this system. Then I will present some recent results on asymptotic revenue equivalence of asymmetric auctions.
Joint work with A. Gavious and N. Gavish.
2015/02/18
14:30-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Nao Hamamuki (Hokkaido University)
Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations (日本語)
Nao Hamamuki (Hokkaido University)
Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations (日本語)
2015/02/18
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Toshio Fukushima (National Astronomical Observatory)
Precise and fast computation of elliptic integrals and elliptic functions (日本語)
Toshio Fukushima (National Astronomical Observatory)
Precise and fast computation of elliptic integrals and elliptic functions (日本語)
[ Abstract ]
Summarized is the recent progress of the methods to compute (i) Legendre's normal form complete elliptic integrals of all three kinds, $K(m)$, $E(m)$, and $\Pi(n|m)$, (ii) Legendre's normal form incomplete elliptic integrals of all three kinds, $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$, (iii) Jacobian elliptic functions, $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $\mathrm{dn}(u|m)$, and $\mathrm{am}(u|m)$, (iv) the inverse functions of $K(m)$ and $E(m)$, $m_K(K)$ and $m_E(E)$, (v) the inverse of a general incomplete elliptic integral in Jacobi's form, $G(\mathrm{am}(u|m),n|m)$, with respect to $u$, and (vi) the partial derivatives of $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $dn(u|m)$, $E(\mathrm{am}(u|m)|m)$, and $\Pi(\mathrm{am}(u|m),n|m)$ with respect to $u$ and those of $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$ with respect to $\phi$. In order to avoid the information loss when $n\ll 1$ and/or $m \ll 1$, focused are the associate incomplete elliptc integrals defined as $B(\phi|m)=[E(\phi|m)-(1-m)F(\phi|m)]/m$, $D(\phi|m)=[F(\phi|m)-E(\phi|m)]/m$, and $J(\phi,n|m)=[\Pi(\phi,n|m)-F(\phi|m)]/n$, and their complete versions, $B(m)=[E(m)-(1-m)K(m)]/m$, $D(m)=[K(m)-E(m)]/m$, and $J(n|m)=[\Pi(n|m)-K(m)]/n$. The main techniques used are (i) the piecewise approximation for single variable functions as $K(m)$, and (ii) the combination of repeated usage of the half and double argument transformations and the truncated Maclaurin series expansions with respect to $u = F(\phi|m)$. The new methods are of the full double precision accuracy without any chance of cancellation against small input arguments. They run significantly faster than the existing methods: (i) 2.5 times faster than Cody's Chebyshev polynomial approximations for $K(m)$ and $E(m)$, (ii) 2.5 times faster than Bulirsch's cel for $\Pi(n|m)$, (iii) slightly faster than Bulirsch's el1 for $F(\phi|m)$, (iv) 3.5 times faster than Carlson's $R_D$ for $E(\phi|m)$, (v) 3.5 times faster than Carlson's $R_C$, $R_D$, $R_F$, and $R_J$ for $\Pi(\phi,n|m)$, and (vi) 1.5 times faster than Bulirsch's \texttt{sncndn} for $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, and $\mathrm{dn}(u|m)$.
Summarized is the recent progress of the methods to compute (i) Legendre's normal form complete elliptic integrals of all three kinds, $K(m)$, $E(m)$, and $\Pi(n|m)$, (ii) Legendre's normal form incomplete elliptic integrals of all three kinds, $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$, (iii) Jacobian elliptic functions, $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $\mathrm{dn}(u|m)$, and $\mathrm{am}(u|m)$, (iv) the inverse functions of $K(m)$ and $E(m)$, $m_K(K)$ and $m_E(E)$, (v) the inverse of a general incomplete elliptic integral in Jacobi's form, $G(\mathrm{am}(u|m),n|m)$, with respect to $u$, and (vi) the partial derivatives of $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $dn(u|m)$, $E(\mathrm{am}(u|m)|m)$, and $\Pi(\mathrm{am}(u|m),n|m)$ with respect to $u$ and those of $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$ with respect to $\phi$. In order to avoid the information loss when $n\ll 1$ and/or $m \ll 1$, focused are the associate incomplete elliptc integrals defined as $B(\phi|m)=[E(\phi|m)-(1-m)F(\phi|m)]/m$, $D(\phi|m)=[F(\phi|m)-E(\phi|m)]/m$, and $J(\phi,n|m)=[\Pi(\phi,n|m)-F(\phi|m)]/n$, and their complete versions, $B(m)=[E(m)-(1-m)K(m)]/m$, $D(m)=[K(m)-E(m)]/m$, and $J(n|m)=[\Pi(n|m)-K(m)]/n$. The main techniques used are (i) the piecewise approximation for single variable functions as $K(m)$, and (ii) the combination of repeated usage of the half and double argument transformations and the truncated Maclaurin series expansions with respect to $u = F(\phi|m)$. The new methods are of the full double precision accuracy without any chance of cancellation against small input arguments. They run significantly faster than the existing methods: (i) 2.5 times faster than Cody's Chebyshev polynomial approximations for $K(m)$ and $E(m)$, (ii) 2.5 times faster than Bulirsch's cel for $\Pi(n|m)$, (iii) slightly faster than Bulirsch's el1 for $F(\phi|m)$, (iv) 3.5 times faster than Carlson's $R_D$ for $E(\phi|m)$, (v) 3.5 times faster than Carlson's $R_C$, $R_D$, $R_F$, and $R_J$ for $\Pi(\phi,n|m)$, and (vi) 1.5 times faster than Bulirsch's \texttt{sncndn} for $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, and $\mathrm{dn}(u|m)$.
2015/01/19
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshitaka Watanabe (Kyushu University)
Between error and residual in numerical computations (日本語)
Yoshitaka Watanabe (Kyushu University)
Between error and residual in numerical computations (日本語)
2014/12/01
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yusuke Imoto (Kyushu University)
An error estimate of a generalized particle method for Poisson equations
(日本語)
[ Reference URL ]
http://www.infsup.jp/utnas/
Yusuke Imoto (Kyushu University)
An error estimate of a generalized particle method for Poisson equations
(日本語)
[ Reference URL ]
http://www.infsup.jp/utnas/
2014/10/20
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Guanyu Zhou (The University of Tokyo)
Finite element method with various types of penalty on domain/boundary (ENGLISH)
Guanyu Zhou (The University of Tokyo)
Finite element method with various types of penalty on domain/boundary (ENGLISH)
[ Abstract ]
We are concerned with several penalty methods (on domain/boundary)
combining with finite element method to solve some partial differential equations. The penalty methods are very useful and widely applied to various problems. For example, to solve the Navier-Stokes equations in moving boundary domain, the finite element method requires to construct the boundary fitted mesh at every times step, which is very time-consuming. The fictitious domain method is proposed to tackle this problem. It is to reformulate the equation to a larger fixed domain, called the fictitious domain, to which we can take a uniform mesh independent on the original moving boundary. The reformulation is based on a penalty method on do- main. Some penalty methods are proposed to approximate the boundary conditions which are not easy to handle with general FEM, such as the slip boundary condition to Stokes/Navier-Stokes equations, the unilateral boundary condition of Signorini’s type to Stokes equations, and so on. It is known that the variational crimes occurs if the finite element spaces or the implementation methods are not chosen properly for slip boundary condition. By introducing a penalty term to the normal component of velocity on slip boundary, we can solve the equations in FEM easily. For the boundary of Signorini’s type, the variational form is an inequality, to which the FEM is not easy to applied. However, we can approximate the variational inequality by a variation equation with penalty term, which can be solve by FEM directly. In above, we introduced several penalty methods with finite element approximation. In this work, we investigate the well-posedness of those penalty method, and obtain the error estimates of penalty; moreover, we consider the penalty methods combining with finite element approximation and show the error estimates.
We are concerned with several penalty methods (on domain/boundary)
combining with finite element method to solve some partial differential equations. The penalty methods are very useful and widely applied to various problems. For example, to solve the Navier-Stokes equations in moving boundary domain, the finite element method requires to construct the boundary fitted mesh at every times step, which is very time-consuming. The fictitious domain method is proposed to tackle this problem. It is to reformulate the equation to a larger fixed domain, called the fictitious domain, to which we can take a uniform mesh independent on the original moving boundary. The reformulation is based on a penalty method on do- main. Some penalty methods are proposed to approximate the boundary conditions which are not easy to handle with general FEM, such as the slip boundary condition to Stokes/Navier-Stokes equations, the unilateral boundary condition of Signorini’s type to Stokes equations, and so on. It is known that the variational crimes occurs if the finite element spaces or the implementation methods are not chosen properly for slip boundary condition. By introducing a penalty term to the normal component of velocity on slip boundary, we can solve the equations in FEM easily. For the boundary of Signorini’s type, the variational form is an inequality, to which the FEM is not easy to applied. However, we can approximate the variational inequality by a variation equation with penalty term, which can be solve by FEM directly. In above, we introduced several penalty methods with finite element approximation. In this work, we investigate the well-posedness of those penalty method, and obtain the error estimates of penalty; moreover, we consider the penalty methods combining with finite element approximation and show the error estimates.
2014/07/28
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Miyaji (RIMS, Kyoto University)
Computer assisted analysis of Craik’s and Pehlivan’s 3D dynamical systems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Tomoyuki Miyaji (RIMS, Kyoto University)
Computer assisted analysis of Craik’s and Pehlivan’s 3D dynamical systems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2014/06/09
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Issei Oikawa (Waseda University)
A hybridized discontinuous Galerkin method with weak stabilization (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Issei Oikawa (Waseda University)
A hybridized discontinuous Galerkin method with weak stabilization (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2014/05/12
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Chien-Hong Cho (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
http://www.infsup.jp/utnas/
Chien-Hong Cho (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
[ Abstract ]
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
[ Reference URL ]We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
http://www.infsup.jp/utnas/
2014/04/21
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takashi Nakazawa (Tohoku University)
Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Takashi Nakazawa (Tohoku University)
Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2014/02/13
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mitchell Luskin (University of Minnesota)
Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)
http://www.infsup.jp/utnas/
Mitchell Luskin (University of Minnesota)
Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)
[ Abstract ]
The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.
Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.
[ Reference URL ]The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.
Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.
http://www.infsup.jp/utnas/
2014/01/28
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Hideki Murakawa (Kyushu University)
Mathematical models of cell-cell adhesion (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Hideki Murakawa (Kyushu University)
Mathematical models of cell-cell adhesion (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2013/11/12
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Takahito Kashiwabara (The University of Tokyo)
Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Takahito Kashiwabara (The University of Tokyo)
Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2013/10/29
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Sei-ichiro Nagoya (ARK Information Systems)
Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Sei-ichiro Nagoya (ARK Information Systems)
Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2013/07/23
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Akira Sasamoto (National Institute of Advanced Industrial Science and Technology)
Boundary Integral Equation Method for several Laplace equations with crack(s) (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Akira Sasamoto (National Institute of Advanced Industrial Science and Technology)
Boundary Integral Equation Method for several Laplace equations with crack(s) (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2013/07/16
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Karel Svadlenka (Kanazawa University)
Numerical computation of motion of interface networks (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Karel Svadlenka (Kanazawa University)
Numerical computation of motion of interface networks (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2013/07/02
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Masaru Miyashita (Sumitomo Heavy Industries, Ltd.)
Numerical plasma simulation for reactive plasma deposition (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Masaru Miyashita (Sumitomo Heavy Industries, Ltd.)
Numerical plasma simulation for reactive plasma deposition (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
