amg_globals.m

五点差分型多重网格方法：各种插值算子的比较）

%AMG_GLOBALS contains global variables and flags for the AMG algorithm

% Ryan McKenzie
% Department of Computational Sciences
% University of Kentucky

%Global definitions for yes and no
global YES; YES=1;
global NO; NO = 0;

%Global flags for setup options
global PROB_SRC %What is the source for the problem
    global USER_SPEC_FD; USER_SPEC_FD = 11; %user defined finite difference
    global USER_SPEC_FEM; USER_SPEC_FEM = 12; %user defined finite element
    global EXAMPLE1; EXAMPLE1 = 13; %finite difference poisson
    
global PLOT_ACTUAL; %whether or not to calculate and plot actual solution
global SHOW_PROFILE; %whether or not to show the function profiler
    
global PROB_TYPE %How many data points to solve over
    global STIFFNESS; STIFFNESS = 101;
    global ELEMENTS; ELEMENTS = 102;

global SETUP_ALG %Which coarse point selector and intergrid weight generator to use
    global RUGE_STUEBEN; RUGE_STUEBEN = 201;
    global AMGm; AMGm = 202;
    global SMOOTH_AGGREGATE; SMOOTH_AGGREGATE = 203;
    
global CYCLE_TYPE %What "shape" of recursive cycle to use
    global VCYCLE; VCYCLE = 301;
    global WCYCLE; WCYCLE = 302;
    global FCYCLE; FCYCLE = 303;
    
global SETUP_OPT %When to perform the setup
    global AT_ONCE; AT_ONCE = 401;
    global AT_EACH; AT_EACH = 402;

%Global flags for AMG options
global SMOOTHER %which smoother to use
    global JACOBI; JACOBI = 501;
    global SOR; SOR = 502;

global C_SOLVER %which solver to use on coarsest level
    global THE_SMOOTHER; THE_SMOOTHER = 601;
    global DIRECT_ELIM; DIRECT_ELIM = 602;
    
global POST_SMOOTH %do we post-smooth at each level

global STOP_TYPE %which type of stopping criteria to check for
    global RESID_THRESHOLD; RESID_THRESHOLD = 701;
    global RESID_REDUCE; RESID_REDUCE = 702;
    global MAX_ITRS; MAX_ITRS = 703;
    
global STOP_VALUE; %value for stopping criteria
global ABSOLUTE_MAX_ITRS; %max smoother iterations to execute if stopping criteria not met

%Global variables for use in AMG algorithm
global FINEPOINTS; %number of data points in finest grid (FD or FEM)
global MAXVERTEX; %number of vertices attached to each finite element
global PAIRS; %local node numberings for FEM
global COARSEST; %coarsest level 
global CYCLES; %number of complete recursive cycles to perform

global A; %structure to contain system matrices
%structure elements
% A( x ).matrix - system coefficient matrix at level x (FD)
% A( x ).elements - element matrices for nodes at level x (FEM)
% A( x ).elconn - element connectivity matrix for nodes at level x (FEM)
% A( x ).edges - edge matrices for nodes at level x (FEM)
% A( x ).edconn - edge connectivity matrix for nodes at level x (FEM)

global W; %structure to contain interpolation weights
%structure elements
% W( x ).weight - The intergrid transfer weight between levels x and x+1
% W( x ).molecules - The intergrid transfer molecules between levels x and x+1

global SW_BOUND; %boundary between what are considered strong and weak connections
%this factor must be bounded between 0 and 1

global X_Guess; %input initial guess
global RHS; %input right hand side
global SOLN; %computed result

%Global variables to store interesting analysis data
global INIT_RESID; %stores 2-norm of initial residual
global FINAL_RESID; %stores 2-norm of final residual
global RH1; %2-D stores a history of the 2-norm residual before correction [ RH1(i,j) = resid1 at cycle i level j ]
global RH2; %2-D stores a history of the 2-norm residual after correction [ RH2(i,j) = resid2 at cycle i level j ]
global IH1; %2-D stores a history of the number of pre-smoothing iterations [ IH1(i,j) = #itrs at cycle i level j ]
global IH2; %2-D stores a history of the number of post-smoothing iterations [ IH2(i,j) = #itrs at cycle i level j ]