/*@C
PetscViewerDrawGetDrawLG - Returns PetscDrawLG object from PetscViewer object.
This PetscDrawLG object may then be used to perform graphics using
PetscDrawLGXXX() commands.
Not Collective (but PetscDrawLG object will be parallel if PetscViewer is)
Input Parameter:
+ PetscViewer - the PetscViewer (created with PetscViewerDrawOpen())
- windownumber - indicates which subwindow (usually 0)
Ouput Parameter:
. draw - the draw line graph object
Level: intermediate
Concepts: line graph^accessing context
.seealso: PetscViewerDrawGetDraw(), PetscViewerDrawGetAxis(), PetscViewerDrawOpen()
@*/
PetscErrorCode PETSC_DLLEXPORT PetscViewerDrawGetDrawLG(PetscViewer viewer,PetscInt windownumber,PetscDrawLG *drawlg)
{
PetscErrorCode ierr;
PetscTruth isdraw;
PetscViewer_Draw *vdraw = (PetscViewer_Draw*)viewer->data;
PetscFunctionBegin;
PetscValidHeaderSpecific(viewer,PETSC_VIEWER_COOKIE,1);
PetscValidPointer(drawlg,3);
ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
if (!isdraw) {
SETERRQ(PETSC_ERR_ARG_WRONG,"Must be draw type PetscViewer");
}
if (windownumber < 0) {
SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Window number cannot be negative");
}
if (windownumber+vdraw->draw_base >= vdraw->draw_max || !vdraw->draw[windownumber+vdraw->draw_base]) {
ierr = PetscViewerDrawGetDraw(viewer,windownumber,PETSC_NULL);CHKERRQ(ierr);
}
if (!vdraw->drawlg[windownumber+vdraw->draw_base]) {
ierr = PetscDrawLGCreate(vdraw->draw[windownumber+vdraw->draw_base],1,&vdraw->drawlg[windownumber+vdraw->draw_base]);CHKERRQ(ierr);
ierr = PetscLogObjectParent(viewer,vdraw->drawlg[windownumber+vdraw->draw_base]);CHKERRQ(ierr);
}
*drawlg = vdraw->drawlg[windownumber+vdraw->draw_base];
PetscFunctionReturn(0);
}
/*@C
PetscViewerDrawGetDrawLG - Returns PetscDrawLG object from PetscViewer object.
This PetscDrawLG object may then be used to perform graphics using
PetscDrawLGXXX() commands.
Collective on PetscViewer
Input Parameter:
+ PetscViewer - the PetscViewer (created with PetscViewerDrawOpen())
- windownumber - indicates which subwindow (usually 0)
Ouput Parameter:
. draw - the draw line graph object
Level: intermediate
Concepts: line graph^accessing context
.seealso: PetscViewerDrawGetDraw(), PetscViewerDrawGetAxis(), PetscViewerDrawOpen()
@*/
PetscErrorCode PetscViewerDrawGetDrawLG(PetscViewer viewer,PetscInt windownumber,PetscDrawLG *drawlg)
{
PetscErrorCode ierr;
PetscBool isdraw;
PetscViewer_Draw *vdraw;
PetscFunctionBegin;
PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,1);
PetscValidLogicalCollectiveInt(viewer,windownumber,2);
PetscValidPointer(drawlg,3);
ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
if (!isdraw) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be draw type PetscViewer");
if (windownumber < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Window number cannot be negative");
vdraw = (PetscViewer_Draw*)viewer->data;
if (windownumber+vdraw->draw_base >= vdraw->draw_max || !vdraw->draw[windownumber+vdraw->draw_base]) {
ierr = PetscViewerDrawGetDraw(viewer,windownumber,NULL);CHKERRQ(ierr);
}
if (!vdraw->drawlg[windownumber+vdraw->draw_base]) {
ierr = PetscDrawLGCreate(vdraw->draw[windownumber+vdraw->draw_base],1,&vdraw->drawlg[windownumber+vdraw->draw_base]);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)viewer,(PetscObject)vdraw->drawlg[windownumber+vdraw->draw_base]);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(vdraw->drawlg[windownumber+vdraw->draw_base]);CHKERRQ(ierr);
}
*drawlg = vdraw->drawlg[windownumber+vdraw->draw_base];
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscDraw draw;
PetscDrawLG lg;
PetscDrawAxis axis;
PetscInt n = 15,i,x = 0,y = 0,width = 400,height = 300,nports = 1;
PetscBool useports,flg;
const char *xlabel,*ylabel,*toplabel,*legend;
PetscReal xd,yd;
PetscDrawViewPorts *ports = NULL;
PetscErrorCode ierr;
toplabel = "Top Label"; xlabel = "X-axis Label"; ylabel = "Y-axis Label"; legend = "Legend";
ierr = PetscInitialize(&argc,&argv,NULL,help);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-x",&x,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-y",&y,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-width",&width,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-height",&height,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-nports",&nports,&useports);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-nolegend",&flg);CHKERRQ(ierr);
if (flg) legend = NULL;
ierr = PetscOptionsHasName(NULL,NULL,"-notoplabel",&flg);CHKERRQ(ierr);
if (flg) toplabel = NULL;
ierr = PetscOptionsHasName(NULL,NULL,"-noxlabel",&flg);CHKERRQ(ierr);
if (flg) xlabel = NULL;
ierr = PetscOptionsHasName(NULL,NULL,"-noylabel",&flg);CHKERRQ(ierr);
if (flg) ylabel = NULL;
ierr = PetscOptionsHasName(NULL,NULL,"-nolabels",&flg);CHKERRQ(ierr);
if (flg) {toplabel = NULL; xlabel = NULL; ylabel = NULL;}
ierr = PetscDrawCreate(PETSC_COMM_WORLD,0,"Title",x,y,width,height,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
if (useports) {
ierr = PetscDrawViewPortsCreate(draw,nports,&ports);CHKERRQ(ierr);
ierr = PetscDrawViewPortsSet(ports,0);CHKERRQ(ierr);
}
ierr = PetscDrawLGCreate(draw,1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGSetUseMarkers(lg,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetColors(axis,PETSC_DRAW_BLACK,PETSC_DRAW_RED,PETSC_DRAW_BLUE);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,toplabel,xlabel,ylabel);CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,&legend);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(lg);CHKERRQ(ierr);
for (i=0; i<=n; i++) {
xd = (PetscReal)(i - 5); yd = xd*xd;
ierr = PetscDrawLGAddPoint(lg,&xd,&yd);CHKERRQ(ierr);
}
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
ierr = PetscDrawLGSave(lg);CHKERRQ(ierr);
ierr = PetscDrawViewPortsDestroy(ports);CHKERRQ(ierr);
ierr = PetscDrawLGDestroy(&lg);CHKERRQ(ierr);
ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
PetscDraw draw;
PetscDrawLG lg;
PetscDrawAxis axis;
PetscInt n = 20,i,x = 0,y = 0,width = 300,height = 300,nports = 1;
PetscTruth flg;
const char *xlabel,*ylabel,*toplabel;
PetscReal xd,yd;
PetscDrawViewPorts *ports;
PetscErrorCode ierr;
xlabel = "X-axis Label";toplabel = "Top Label";ylabel = "Y-axis Label";
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-width",&width,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-height",&height,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-nolabels",&flg);CHKERRQ(ierr);
if (flg) {
xlabel = (char *)0; toplabel = (char *)0;
}
ierr = PetscDrawCreate(PETSC_COMM_SELF,0,"Title",x,y,width,height,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-nports",&nports,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscDrawViewPortsCreate(draw,nports,&ports);CHKERRQ(ierr);
ierr = PetscDrawViewPortsSet(ports,0);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetColors(axis,PETSC_DRAW_BLACK,PETSC_DRAW_RED,PETSC_DRAW_BLUE);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,toplabel,xlabel,ylabel);CHKERRQ(ierr);
for (i=0; i<n ; i++) {
xd = (PetscReal)(i - 5); yd = xd*xd;
ierr = PetscDrawLGAddPoint(lg,&xd,&yd);CHKERRQ(ierr);
}
ierr = PetscDrawLGIndicateDataPoints(lg);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
ierr = PetscDrawString(draw,-3.,150.0,PETSC_DRAW_BLUE,"A legend");CHKERRQ(ierr);
ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
ierr = PetscSleep(2);CHKERRQ(ierr);
ierr = PetscDrawViewPortsDestroy(ports);CHKERRQ(ierr);
ierr = PetscDrawLGDestroy(lg);CHKERRQ(ierr);
ierr = PetscDrawDestroy(draw);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
/*@C
KSPMonitorLGResidualNormCreate - Creates a line graph context for use with
KSP to monitor convergence of preconditioned residual norms.
Collective on KSP
Input Parameters:
+ comm - communicator context
. host - the X display to open, or null for the local machine
. label - the title to put in the title bar
. x, y - the screen coordinates of the upper left coordinate of
the window
- m, n - the screen width and height in pixels
Output Parameter:
. lgctx - the drawing context
Options Database Key:
. -ksp_monitor_lg_residualnorm - Sets line graph monitor
Notes:
Use PetscDrawLGDestroy() to destroy this line graph.
Level: intermediate
.keywords: KSP, monitor, line graph, residual, create
.seealso: KSPMonitorSet(), KSPMonitorLGTrueResidualCreate()
@*/
PetscErrorCode KSPMonitorLGResidualNormCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscDrawLG *lgctx)
{
PetscDraw draw;
PetscErrorCode ierr;
PetscDrawAxis axis;
PetscDrawLG lg;
PetscFunctionBegin;
ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(lg);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Convergence","Iteration","Residual Norm");CHKERRQ(ierr);
ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
*lgctx = lg;
PetscFunctionReturn(0);
}
/*@C
KSPMonitorLGResidualNormCreate - Creates a line graph context for use with
KSP to monitor convergence of preconditioned residual norms.
Collective on KSP
Input Parameters:
+ host - the X display to open, or null for the local machine
. label - the title to put in the title bar
. x, y - the screen coordinates of the upper left coordinate of
the window
- m, n - the screen width and height in pixels
Output Parameter:
. draw - the drawing context
Options Database Key:
. -ksp_monitor_lg_residualnorm - Sets line graph monitor
Notes:
Use KSPMonitorLGResidualNormDestroy() to destroy this line graph; do not use PetscDrawLGDestroy().
Level: intermediate
.keywords: KSP, monitor, line graph, residual, create
.seealso: KSPMonitorLGResidualNormDestroy(), KSPMonitorSet(), KSPMonitorLGTrueResidualCreate()
@*/
PetscErrorCode KSPMonitorLGResidualNormCreate(const char host[],const char label[],int x,int y,int m,int n,PetscObject **objs)
{
PetscDraw win;
PetscErrorCode ierr;
PetscDrawAxis axis;
PetscDrawLG draw;
PetscFunctionBegin;
ierr = PetscDrawCreate(PETSC_COMM_SELF,host,label,x,y,m,n,&win);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(win);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(win,1,&draw);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(draw,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Convergence","Iteration","Residual Norm");CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)draw,(PetscObject)win);CHKERRQ(ierr);
ierr = PetscMalloc1(2,objs);CHKERRQ(ierr);
(*objs)[0] = (PetscObject)draw;
(*objs)[1] = (PetscObject)win;
PetscFunctionReturn(0);
}
/*@C
KSPMonitorSNESLGResidualNormCreate - Creates a line graph context for use with
KSP to monitor convergence of preconditioned residual norms.
Collective on KSP
Input Parameters:
+ comm - communicator context
. host - the X display to open, or null for the local machine
. label - the title to put in the title bar
. x, y - the screen coordinates of the upper left coordinate of
the window
- m, n - the screen width and height in pixels
Output Parameter:
. draw - the drawing context
Options Database Key:
. -ksp_monitor_lg_residualnorm - Sets line graph monitor
Notes:
Use KSPMonitorSNESLGResidualNormDestroy() to destroy this line graph; do not use PetscDrawLGDestroy().
Level: intermediate
.keywords: KSP, monitor, line graph, residual, create
.seealso: KSPMonitorSNESLGResidualNormDestroy(), KSPMonitorSet(), KSPMonitorSNESLGTrueResidualCreate()
@*/
PetscErrorCode KSPMonitorSNESLGResidualNormCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscObject **objs)
{
PetscDraw draw;
PetscErrorCode ierr;
PetscDrawAxis axis;
PetscDrawLG lg;
const char *names[] = {"Linear residual","Nonlinear residual"};
PetscFunctionBegin;
ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,2,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,names);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(lg);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Convergence of Residual Norm","Iteration","Residual Norm");CHKERRQ(ierr);
ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
ierr = PetscMalloc1(2,objs);CHKERRQ(ierr);
(*objs)[1] = (PetscObject)lg;
PetscFunctionReturn(0);
}
/*@C
KSPMonitorSNESLGResidualNormCreate - Creates a line graph context for use with
KSP to monitor convergence of preconditioned residual norms.
Collective on KSP
Input Parameters:
+ host - the X display to open, or null for the local machine
. label - the title to put in the title bar
. x, y - the screen coordinates of the upper left coordinate of
the window
- m, n - the screen width and height in pixels
Output Parameter:
. draw - the drawing context
Options Database Key:
. -ksp_monitor_lg_residualnorm - Sets line graph monitor
Notes:
Use KSPMonitorSNESLGResidualNormDestroy() to destroy this line graph; do not use PetscDrawLGDestroy().
Level: intermediate
.keywords: KSP, monitor, line graph, residual, create
.seealso: KSPMonitorSNESLGResidualNormDestroy(), KSPMonitorSet(), KSPMonitorSNESLGTrueResidualCreate()
@*/
PetscErrorCode KSPMonitorSNESLGResidualNormCreate(const char host[],const char label[],int x,int y,int m,int n,PetscObject **objs)
{
PetscDraw draw;
PetscErrorCode ierr;
PetscDrawAxis axis;
PetscDrawLG drawlg;
const char *names[] = {"Linear residual","Nonlinear residual"};
PetscFunctionBegin;
ierr = PetscDrawCreate(PETSC_COMM_SELF,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,2,&drawlg);CHKERRQ(ierr);
ierr = PetscDrawLGSetFromOptions(drawlg);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(drawlg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Convergence of Residual Norm","Iteration","Residual Norm");CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(drawlg,names);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)drawlg,(PetscObject)draw);CHKERRQ(ierr);
ierr = PetscMalloc1(3,objs);CHKERRQ(ierr);
(*objs)[1] = (PetscObject)drawlg;
(*objs)[2] = (PetscObject)draw;
PetscFunctionReturn(0);
}
/*
Run with -build_twosided allreduce -pc_type bjacobi -sub_pc_type lu -q 16 -ksp_rtol 1.e-34 (or 1.e-14 for double precision)
-q <q> number of spectral elements to use
-N <N> maximum number of GLL points per element
*/
int main(int argc,char **args)
{
PetscErrorCode ierr;
PetscGLL gll;
PetscInt N = 80,n,q = 8,xs,xn,j,l;
PetscReal **A;
Mat K;
KSP ksp;
PC pc;
Vec x,b;
PetscInt *rows;
PetscReal norm,xc,yc,h;
PetscScalar *f;
PetscDraw draw;
PetscDrawLG lg;
PetscDrawAxis axis;
DM da;
PetscMPIInt rank,size;
ierr = PetscInitialize(&argc,&args,NULL,NULL);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-N",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-q",&q,NULL);CHKERRQ(ierr);
ierr = PetscDrawCreate(PETSC_COMM_WORLD,NULL,"Log(Error norm) vs Number of GLL points",0,0,500,500,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
ierr = PetscDrawLGCreate(draw,1,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGSetUseMarkers(lg,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,NULL,"Number of GLL points","Log(Error Norm)");CHKERRQ(ierr);
for (n=4; n<N; n+=2) {
/*
da contains the information about the parallel layout of the elements
*/
ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,q*(n-1)+1,1,1,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,NULL,&q,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
q = (q-1)/(n-1); /* number of spectral elements */
/*
gll simply contains the GLL node and weight values
*/
ierr = PetscGLLCreate(n,PETSCGLL_VIA_LINEARALGEBRA,&gll);CHKERRQ(ierr);
ierr = DMDASetGLLCoordinates(da,&gll);CHKERRQ(ierr);
/*
Creates the element stiffness matrix for the given gll
*/
ierr = PetscGLLElementLaplacianCreate(&gll,&A);CHKERRQ(ierr);
/*
Scale the element stiffness and weights by the size of the element
*/
h = 2.0/q;
for (j=0; j<n; j++) {
gll.weights[j] *= .5*h;
for (l=0; l<n; l++) {
A[j][l] = 2.*A[j][l]/h;
}
}
/*
Create the global stiffness matrix and add the element stiffness for each local element
*/
ierr = DMCreateMatrix(da,&K);CHKERRQ(ierr);
ierr = MatSetOption(K,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
xs = xs/(n-1);
xn = xn/(n-1);
ierr = PetscMalloc1(n,&rows);CHKERRQ(ierr);
/*
loop over local elements
*/
for (j=xs; j<xs+xn; j++) {
for (l=0; l<n; l++) rows[l] = j*(n-1)+l;
ierr = MatSetValues(K,n,rows,n,rows,&A[0][0],ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCreateVecs(K,&x,&b);CHKERRQ(ierr);
ierr = ComputeRhs(da,&gll,b);CHKERRQ(ierr);
/*
Replace the first and last rows/columns of the matrix with the identity to obtain the zero Dirichlet boundary conditions
*/
rows[0] = 0;
rows[1] = q*(n-1);
ierr = MatZeroRowsColumns(K,2,rows,1.0,x,b);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,K,K);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* compute the error to the continium problem */
ierr = ComputeSolution(da,&gll,b);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,b);CHKERRQ(ierr);
/* compute the L^2 norm of the error */
ierr = VecGetArray(x,&f);CHKERRQ(ierr);
ierr = PetscGLLIntegrate(&gll,f,&norm);CHKERRQ(ierr);
ierr = VecRestoreArray(x,&f);CHKERRQ(ierr);
norm = PetscSqrtReal(norm);
ierr = PetscViewerASCIIPrintf(PETSC_VIEWER_STDOUT_WORLD,"L^2 norm of the error %D %g\n",n,(double)norm);CHKERRQ(ierr);
if (n > 10 && norm > 1.e-8) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Slower convergence than expected");
xc = (PetscReal)n;
yc = PetscLog10Real(norm);
ierr = PetscDrawLGAddPoint(lg,&xc,&yc);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = MatDestroy(&K);CHKERRQ(ierr);
ierr = PetscGLLElementLaplacianDestroy(&gll,&A);CHKERRQ(ierr);
ierr = PetscGLLDestroy(&gll);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
}
ierr = PetscDrawLGDestroy(&lg);CHKERRQ(ierr);
ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
