Authors:  
   
   Peijun Li  (lipeijun@math.purdue.edu) 
   Xiaokai Yuan (yuan170@math.purdue.edu)
   Department of Mathematics
   Purdue University, West Lafayette 
   
   Copyright (c) 2019. All Rights Reserved.

   This file is the documentation for DirectSolver2D, a FreeFEM
   subroutine for simulating the scattering of a plane wave by 
   an inhomogeneous medium using the finite element method (FEM). 

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software Foundation,
   Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


                README file for DirectSolver2D  07/16/2019


   DirectSolver2D is a FreeFEM subroutine for simulating the scattering of a plane 
   wave by an inhomogeneous medium using the finite element method (FEM). 

   Please go to the FreeFEM homepage 

                           https://freefem.org/ 
   and download 
                           FreeFem++-cs Windows

   This program can be used to solve the following scattering problems: 

   --------------------------------------------------------------------
   
         { acoustic waves
   Waves {
         { elastic waves 
  
                    { periodic surfaces
   Problem geometry { impenetrable obstacles
                    { penetrable media

                                { perfectly matched layer (PML) 
   Methods of domain truncation {
                                { transparent boundary condition (TBC)

              { uniform meshes
   FEM meshes {
              { adaptive meshes

   ---------------------------------------------------------------------

   NOTE: Please include the following references in any work that utilizes
         this code:

        (1) P. Li and X. Yuan, An adaptive finite element DtN method for the elastic wave scattering problem, Numer. Math., 150 (2022), 993-1033.

        (2) P. Li and X. Yuan, Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structures, Comput. Methods Appl. Mech. Engrg., 360 (2020), 112722.
 
        (3)  X. Jiang, P. Li, J. Lv, and W. Zheng, An adaptive finite element 
             method for the wave scattering with transparentboundary condition, 
             J. Sci. Comput., 72 (2017), 936-956.
         
        (4)  Z. Wang, G. Bao, J. Li, P. Li, and H. Wu, An adaptive finite element 
             method for the diffraction grating problemwith transparent boundary 
             condition, SIAM J. Numer. Anal., 53 (2015), 1585-1607.