Multiscale Mathematics Research Project


Articles

  1. J. Tinsley Oden, S. Prudhomme, A. Romkes, and P. Bauman, Multiscale modeling of physical phenomena: Adaptive control of models, SIAM Journal on Scientific Computing, vol. 28, No 6, 2359-2389 (2006). 
    

    
  2.  J. Tinsley Oden, S. Prudhomme, and P. Bauman,
         Error control for molecular statics problems,
          International Journal for Multiscale Computational 
         Engineering, 
         vol. 4, No 5-6, 647-662 (2007).

    
    

    
  3.  P.T. Bauman, H. Ben Dhia, N. Elkhodja, J.T. Oden, and S. Prudhomme,
         
         On the application of the Arlequin method to the coupling of 
         particle and continuum Models,
          Computational Mechanics, 
         Vol. 42, 511-530 (2008).

    
    

    
  4.  S. Prudhomme, H. Ben Dhia, P.T. Bauman, N. Elkhodja,  and J.T. Oden,
         
         Computational Analysis of Modeling Error for 
         the Coupling of Particle and Continuum Models by the Arlequin Method,
          Computer Methods in Applied Mechanics and Engineering, 
         Vol. 197, 3399-3409 (2008).

    
    

    
  5.  L. Chamoin, J.T. Oden, and S. Prudhomme, 
         
         Numerical Analysis of Modeling Error for 
         the Coupling of Particle and Continuum Models by the Arlequin Method,
          Computer Methods in Applied Mechanics and Engineering, 
         Vol. 197, 3530-3546 (2008).

    
    

    
  6.  P.T. Bauman, J.T. Oden, and S. Prudhomme,
         Adaptive multiscale modeling of polymeric materials: Arlequin coupling
         and goals algorithms,
          Computer Methods in Applied Mechanics and Engineering, 
         Submitted (2008).

    
    

    
  7.  S. Prudhomme, L. Chamoin, H. Ben Dhia, and P.T. Bauman, 
          An adaptive strategy for the control of modeling 
          error in two-dimensional atomic-to-continuum coupling simulations,
          Computer Methods in Applied Mechanics and Engineering, 
         Accepted (2008).

    
    

    
  8.  L. Chamoin, S. Prudhomme, H. Ben Dhia, and P.T. Bauman, and J.T. Oden, 
          Ghost forces and spurious effects in 
          atomic-to-continuum coupling methods by the Arlequin approach,
          International Journal for Numerical Methods in Engineering, 
         In preparation (2008).

    
    

    
  9.  L. Chamoin, S. Prudhomme, and J.T. Oden, 
         On coupling atomic and continuum models with random data 
         by a stochastic collocation method,
          , 
         In preparation (2008).

    
    

    
  10.  S. Prudhomme, L. Chamoin, H. Ben Dhia, and P.T. Bauman, and J.T. Oden,
          Introduction of an averaging operator 
          for atomic-to-continuum coupling methods by the Arlequin approach,
          Computer Methods in Applied Mechanics and Engineering, 
         In preparation (2008).

    
       

    


    Preprints / Reports


    
           
    
  1.  J. Tinsley Oden, S. Prudhomme, A. Romkes, and P. Bauman,
         Multi-scale modeling of physical phenomena: Adaptive 
         control of models,
          
         ICES Report 05-13 and 5-20, May 2005.
    
    

    
  2.  S. Prudhomme, P. Bauman, and J. Tinsley Oden, 
         Error control for molecular statics problems,
          
         ICES Report 05-37, August 2005.

    
    

    
  3.  C. Jhurani and L. Demkowicz, 
         A goal-oriented hp-adaptive dimensional reduction method 
         for one-dimensional network of linear springs, 
          
         ICES Report 06-15, 2006. 

    
    

    
  4.  P.T. Bauman, H. Ben Dhia, N. Elkhodja, J.T. Oden, and S. Prudhomme, 
         On the application of the Arlequin 
         method to the coupling of particle and continuum Models, 
          
         ICES Report 07-28, 2007. 

    
    

    
  5.  L. Chamoin, J.T. Oden, and S. Prudhomme, 
         A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations, 
          
         ICES Report 08-02, 2008. 

    
    

    
  6.  P.T. Bauman, J.T. Oden, and S. Prudhomme, 
         Adaptive multiscale modeling of polymeric materials with Arlequin, 
          
         ICES Report 08-17, 2008. 


    
       


    


    Dissertations


    
           
    
  1.  P. Bauman, 
    
    Adaptive Multiscale Modeling of Polymeric Materials Using Goal-Oriented Error Estimation, 
    Arlequin Coupling, and Goals Algorithms. 
    PhD dissertation, The University of Texas at Austin, 2008. 

    
    

    
  2.  C. Jhurani, 
    
    Multiscale Modeling Using Goal-Oriented Adaptivity and 
    Numerical Homogenization. 
    PhD dissertation proposal, 2008.