static void
redraw_region (GdkRectangle *rect)
{
int eleft, eright, etop, ebottom;
BoxType region;
render_priv *priv = gport->render_priv;
if (!gport->pixmap)
return;
if (rect != NULL)
{
priv->clip_rect = *rect;
priv->clip = true;
}
else
{
priv->clip_rect.x = 0;
priv->clip_rect.y = 0;
priv->clip_rect.width = gport->width;
priv->clip_rect.height = gport->height;
priv->clip = false;
}
set_clip (priv, priv->bg_gc);
set_clip (priv, priv->offlimits_gc);
set_clip (priv, priv->mask_gc);
set_clip (priv, priv->grid_gc);
region.X1 = MIN(Px(priv->clip_rect.x),
Px(priv->clip_rect.x + priv->clip_rect.width + 1));
region.Y1 = MIN(Py(priv->clip_rect.y),
Py(priv->clip_rect.y + priv->clip_rect.height + 1));
region.X2 = MAX(Px(priv->clip_rect.x),
Px(priv->clip_rect.x + priv->clip_rect.width + 1));
region.Y2 = MAX(Py(priv->clip_rect.y),
Py(priv->clip_rect.y + priv->clip_rect.height + 1));
region.X1 = MAX (0, MIN (PCB->MaxWidth, region.X1));
region.X2 = MAX (0, MIN (PCB->MaxWidth, region.X2));
region.Y1 = MAX (0, MIN (PCB->MaxHeight, region.Y1));
region.Y2 = MAX (0, MIN (PCB->MaxHeight, region.Y2));
eleft = Vx (0);
eright = Vx (PCB->MaxWidth);
etop = Vy (0);
ebottom = Vy (PCB->MaxHeight);
if (eleft > eright)
{
int tmp = eleft;
eleft = eright;
eright = tmp;
}
if (etop > ebottom)
{
int tmp = etop;
etop = ebottom;
ebottom = tmp;
}
if (eleft > 0)
gdk_draw_rectangle (gport->drawable, priv->offlimits_gc,
1, 0, 0, eleft, gport->height);
else
eleft = 0;
if (eright < gport->width)
gdk_draw_rectangle (gport->drawable, priv->offlimits_gc,
1, eright, 0, gport->width - eright, gport->height);
else
eright = gport->width;
if (etop > 0)
gdk_draw_rectangle (gport->drawable, priv->offlimits_gc,
1, eleft, 0, eright - eleft + 1, etop);
else
etop = 0;
if (ebottom < gport->height)
gdk_draw_rectangle (gport->drawable, priv->offlimits_gc,
1, eleft, ebottom, eright - eleft + 1,
gport->height - ebottom);
else
ebottom = gport->height;
gdk_draw_rectangle (gport->drawable, priv->bg_gc, 1,
eleft, etop, eright - eleft + 1, ebottom - etop + 1);
ghid_draw_bg_image();
hid_expose_callback (&ghid_hid, ®ion, 0);
ghid_draw_grid ();
/* In some cases we are called with the crosshair still off */
if (priv->attached_invalidate_depth == 0)
DrawAttached ();
/* In some cases we are called with the mark still off */
if (priv->mark_invalidate_depth == 0)
DrawMark ();
draw_lead_user (priv);
priv->clip = false;
/* Rest the clip for bg_gc, as it is used outside this function */
gdk_gc_set_clip_mask (priv->bg_gc, NULL);
}
int ct_stab_parse(const char *ofile, int option, ...)
{
FILE *fp;
if ( ! (fp = fopen(ofile, "rb")) ) {
#ifdef __CYGWIN32__
const char *suffixes[] = { ".exe", ".com", 0 };
int i;
for ( i = 0; suffixes[i]; i ++ ) {
char op[MAXPATHLEN + 1];
strcpy(op, ofile);
strcat(op, suffixes[i]);
if ( (fp = fopen(op, "rb")) )
break;
}
if ( ! suffixes[i] )
#endif
{
fprintf(stderr, "ct_stab_parse: cannot open '%s'\n", ofile);
return -1;
}
}
#define Pm(x) fprintf(stderr, "%s\n", (char *) (x));
#define Pu(x) fprintf(stderr, "%s = %lu\n", #x, (unsigned long) (x))
#define Px(x) fprintf(stderr, "%s = %08lx\n", #x, (unsigned long) (x))
#define Ps(x) fprintf(stderr, "%s = \"%s\"\n", #x, (char *) (x))
#define Pss(x,s) fprintf(stderr, "%s = \"%*s\"\n", #x, (int) (s), (char *) (x))
#if 0
{
struct external_filehdr fh;
fseek(fp, 0, 0);
fread(&fh, sizeof(fh), 1, fp);
Pm("external_filehdr");
Px(fh.f_magic);
Px(fh.f_nscns);
Px(fh.f_timdat);
Px(fh.f_symptr);
Px(fh.f_nsyms);
Px(fh.f_opthdr);
Px(fh.f_flags);
}
{
AOUTHDR fh;
fseek(fp, 0, 0);
fread(&fh, sizeof(fh), 1, fp);
Pm("AOUTHDR");
Px(fh.magic);
Px(fh.vstamp);
Px(fh.tsize);
Px(fh.dsize);
Px(fh.bsize);
Px(fh.entry);
Px(fh.text_start);
Px(fh.data_start);
}
#endif
{
FILHDR fh;
fseek(fp, 0, 0);
fread(&fh, sizeof(fh), 1, fp);
Pm("FILHDR");
Px(fh.e_magic);
Px(fh.e_cblp);
Px(fh.e_cp);
Px(fh.e_crlc);
Px(fh.e_cparhdr);
Px(fh.e_minalloc);
Px(fh.e_maxalloc);
Px(fh.e_ss);
Px(fh.e_sp);
Px(fh.e_csum);
Px(fh.e_ip);
Px(fh.e_cs);
Px(fh.e_lfarlc);
Px(fh.e_ovno);
/* fh.e_res[4][2] */
Px(fh.e_oemid);
Px(fh.e_oeminfo);
/* fh.e_res2[10][2] */
Px(fh.e_lfanew);
/* fh.dos_message[16][4] */
Px(fh.nt_signature);
Pm("From standard header");
Px(fh.f_magic);
Px(fh.f_nscns);
Px(fh.f_timdat);
Px(fh.f_symptr);
Px(fh.f_nsyms);
Px(fh.f_opthdr);
Px(fh.f_flags);
// exit (1);
fseek(fp, fh.f_opthdr, SEEK_CUR);
{
int i;
Pm("Sections");
for ( i = 0; i < fh.f_nscns; i ++ ) {
SCNHDR sh;
fread(&sh, sizeof(sh), 1, fp);
Pm("");
Pss(sh.s_name, sizeof(sh.s_name));
Px(sh.s_paddr);
Px(sh.s_vaddr);
Pu(sh.s_size);
#if 0
Px(sh.s_scnptr);
Px(sh.s_relptr);
Pu(sh.s_nreloc);
Pu(sh.s_nlnno);
Px(sh.s_flags);
#endif
}
}
if ( fh.f_opthdr == sizeof(AOUTHDR) ) {
AOUTHDR aoh;
Pm("AOUTHDR");
fread(&aoh, sizeof(aoh), 1, fp);
Px(aoh.magic);
Px(aoh.vstamp);
Px(aoh.tsize);
Px(aoh.dsize);
Px(aoh.bsize);
Px(aoh.entry);
Px(aoh.text_start);
Px(aoh.data_start);
}
exit(1);
{
int i;
fseek(fp, fh.f_symptr, 0);
Pm("Reading symbols");
for ( i = 0; i < fh.f_nsyms; i ++ ) {
SYMENT se;
fread(&se, sizeof(se), 1, fp);
// Ps(se.e.e_name);
if ( se.e.e.e_zeroes ) {
Ps(se.e.e_name);
} else {
Px(se.e.e.e_zeroes);
Px(se.e.e.e_offset);
}
Px(se.e_value);
Px(se.e_scnum);
Px(se.e_type);
Px(se.e_sclass[0]);
Px(se.e_numaux[1]);
}
}
}
fclose(fp);
return 0;
}
void Basis_HGRAD_LINE_Hermite_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar & outputValues,
const ArrayScalar & inputPoints,
const EOperator operatorType) const {
// Verify arguments
#ifdef HAVE_INTREPID_DEBUG
Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
inputPoints,
operatorType,
this -> getBaseCellTopology(),
this -> getCardinality() );
#endif
// Number of evaluation points = dim 0 of inputPoints
int nPts = inputPoints.dimension(0);
int nBf = this->getCardinality();
int n = nBf/2;
// Legendre polynomials and their derivatives evaluated on inputPoints
SerialDenseMatrix legendre(nBf,nPts);
// Hermite interpolants evaluated on inputPoints
SerialDenseMatrix hermite(nBf,nPts);
ArrayScalar P (nBf);
ArrayScalar Px(nBf);
int derivative_order;
int derivative_case = static_cast<int>(operatorType);
if( derivative_case == 0 ) {
derivative_order = 0;
}
else if( derivative_case > 0 && derivative_case < 5 ) {
derivative_order = 1;
}
else {
derivative_order = derivative_case - 3;
}
try {
// GRAD,CURL,DIV, and D1 are all the first derivative
switch (operatorType) {
case OPERATOR_VALUE:
{
for( int i=0; i<nPts; ++i ) {
recurrence( P, Px, inputPoints(i,0) );
for( int j=0; j<nBf; ++j ) {
legendre(j,i) = P(j);
}
}
break;
}
case OPERATOR_GRAD:
case OPERATOR_DIV:
case OPERATOR_CURL:
case OPERATOR_D1:
{
for( int i=0; i<nPts; ++i ) {
recurrence( P, Px, inputPoints(i,0) );
for( int j=0; j<nBf; ++j ) {
legendre(j,i) = Px(j);
}
}
break;
}
case OPERATOR_D2:
case OPERATOR_D3:
case OPERATOR_D4:
case OPERATOR_D5:
case OPERATOR_D6:
case OPERATOR_D7:
case OPERATOR_D8:
case OPERATOR_D9:
case OPERATOR_D10:
{
for( int i=0; i<nPts; ++i ) {
legendre_d( P, Px, derivative_order, inputPoints(i,0));
for( int j=0; j<nBf; ++j ) {
legendre(j,i) = Px(j);
}
}
break;
}
default:
TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
">>> ERROR (Basis_HGRAD_LINE_Hermite_FEM): Invalid operator type");
} // switch(operatorType)
}
catch (std::invalid_argument &exception){
TEUCHOS_TEST_FOR_EXCEPTION( true , std::invalid_argument,
">>> ERROR (Basis_HGRAD_LINE_Hermite_FEM): Operator failed");
}
if( !isFactored_ ) {
solver_.factorWithEquilibration(true);
solver_.factor();
}
solver_.setVectors(Teuchos::rcpFromRef(hermite),Teuchos::rcpFromRef(legendre));
solver_.solve();
if(derivative_order > 0)
{
for( int i=0; i<n; ++i ) {
for( int j=0; j<nPts; ++j ) {
outputValues(2*i, j,0) = hermite(i, j);
outputValues(2*i+1,j,0) = hermite(i+n,j);
}
}
}
else {
for( int i=0; i<n; ++i ) {
for( int j=0; j<nPts; ++j ) {
outputValues(2*i ,j) = hermite(i, j);
outputValues(2*i+1,j) = hermite(i+n,j);
}
}
}
} // getValues()
PreconditionerBlockMS<space_type>::PreconditionerBlockMS(space_ptrtype Xh, // (u)x(p)
ModelProperties model, // model
std::string const& p, // prefix
sparse_matrix_ptrtype AA ) // The matrix
:
M_backend(backend()), // the backend associated to the PC
M_Xh( Xh ),
M_Vh( Xh->template functionSpace<0>() ), // Potential
M_Qh( Xh->template functionSpace<1>() ), // Lagrange
M_Vh_indices( M_Vh->nLocalDofWithGhost() ),
M_Qh_indices( M_Qh->nLocalDofWithGhost() ),
M_uin( M_backend->newVector( M_Vh ) ),
M_uout( M_backend->newVector( M_Vh ) ),
M_pin( M_backend->newVector( M_Qh ) ),
M_pout( M_backend->newVector( M_Qh ) ),
U( M_Xh, "U" ),
M_mass(M_backend->newMatrix(M_Vh,M_Vh)),
M_L(M_backend->newMatrix(M_Qh,M_Qh)),
M_er( 1. ),
M_model( model ),
M_prefix( p ),
M_prefix_11( p+".11" ),
M_prefix_22( p+".22" ),
u(M_Vh, "u"),
ozz(M_Vh, "ozz"),
zoz(M_Vh, "zoz"),
zzo(M_Vh, "zzo"),
M_ozz(M_backend->newVector( M_Vh )),
M_zoz(M_backend->newVector( M_Vh )),
M_zzo(M_backend->newVector( M_Vh )),
X(M_Qh, "X"),
Y(M_Qh, "Y"),
Z(M_Qh, "Z"),
M_X(M_backend->newVector( M_Qh )),
M_Y(M_backend->newVector( M_Qh )),
M_Z(M_backend->newVector( M_Qh )),
phi(M_Qh, "phi")
{
tic();
LOG(INFO) << "[PreconditionerBlockMS] setup starts";
this->setMatrix( AA );
this->setName(M_prefix);
/* Indices are need to extract sub matrix */
std::iota( M_Vh_indices.begin(), M_Vh_indices.end(), 0 );
std::iota( M_Qh_indices.begin(), M_Qh_indices.end(), M_Vh->nLocalDofWithGhost() );
M_11 = AA->createSubMatrix( M_Vh_indices, M_Vh_indices, true, true);
/* Boundary conditions */
BoundaryConditions M_bc = M_model.boundaryConditions();
map_vector_field<FEELPP_DIM,1,2> m_dirichlet_u { M_bc.getVectorFields<FEELPP_DIM> ( "u", "Dirichlet" ) };
map_scalar_field<2> m_dirichlet_p { M_bc.getScalarFields<2> ( "phi", "Dirichlet" ) };
/* Compute the mass matrix (needed in first block, constant) */
auto f2A = form2(_test=M_Vh, _trial=M_Vh, _matrix=M_mass);
auto f1A = form1(_test=M_Vh);
f2A = integrate(_range=elements(M_Vh->mesh()), _expr=inner(idt(u),id(u))); // M
for(auto const & it : m_dirichlet_u )
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_11<<"\n";
f2A += on(_range=markedfaces(M_Vh->mesh(),it.first), _expr=it.second,_rhs=f1A, _element=u, _type="elimination_symmetric");
}
/* Compute the L (= er * grad grad) matrix (the second block) */
auto f2L = form2(_test=M_Qh,_trial=M_Qh, _matrix=M_L);
for(auto it : M_model.materials() )
{
f2L += integrate(_range=markedelements(M_Qh->mesh(),marker(it)), _expr=M_er*inner(gradt(phi), grad(phi)));
}
auto f1LQ = form1(_test=M_Qh);
for(auto const & it : m_dirichlet_p)
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_22<<"\n";
f2L += on(_range=markedfaces(M_Qh->mesh(),it.first),_element=phi, _expr=it.second, _rhs=f1LQ, _type="elimination_symmetric");
}
if(soption(_name="pc-type", _prefix=M_prefix_11) == "ams")
#if FEELPP_DIM == 3
{
M_grad = Grad( _domainSpace=M_Qh, _imageSpace=M_Vh);
// This preconditioner is linked to that backend : the backend will
// automatically use the preconditioner.
auto prec = preconditioner(_pc=pcTypeConvertStrToEnum(soption(M_prefix_11+".pc-type")),
_backend=backend(_name=M_prefix_11),
_prefix=M_prefix_11,
_matrix=M_11
);
prec->setMatrix(M_11);
prec->attachAuxiliarySparseMatrix("G",M_grad.matPtr());
if(boption(M_prefix_11+".useEdge"))
{
LOG(INFO) << "[ AMS ] : using SetConstantEdgeVector \n";
ozz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(1),cst(0),cst(0)));
zoz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(1),cst(0)));
zzo.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(0),cst(1)));
*M_ozz = ozz; M_ozz->close();
*M_zoz = zoz; M_zoz->close();
*M_zzo = zzo; M_zzo->close();
prec->attachAuxiliaryVector("Px",M_ozz);
prec->attachAuxiliaryVector("Py",M_zoz);
prec->attachAuxiliaryVector("Pz",M_zzo);
}
else
{
LOG(INFO) << "[ AMS ] : using SetCoordinates \n";
X.on(_range=elements(M_Vh->mesh()),_expr=Px());
Y.on(_range=elements(M_Vh->mesh()),_expr=Py());
Z.on(_range=elements(M_Vh->mesh()),_expr=Pz());
*M_X = X; M_X->close();
*M_Y = Y; M_Y->close();
*M_Z = Z; M_Z->close();
prec->attachAuxiliaryVector("X",M_X);
prec->attachAuxiliaryVector("Y",M_Y);
prec->attachAuxiliaryVector("Z",M_Z);
}
}
#else
std::cerr << "ams preconditioner is not interfaced in two dimensions\n";
#endif
toc( "[PreconditionerBlockMS] setup done ", FLAGS_v > 0 );
}
PfxBool pfxIntersectRayCapsule(const PfxRayInput &ray,PfxRayOutput &out,const PfxCapsule &capsule,const PfxTransform3 &transform)
{
// レイをCapsuleのローカル座標へ変換
PfxTransform3 transformCapsule = orthoInverse(transform);
PfxVector3 startPosL = transformCapsule.getUpper3x3() * ray.m_startPosition + transformCapsule.getTranslation();
PfxVector3 rayDirL = transformCapsule.getUpper3x3() * ray.m_direction;
PfxFloat radSqr = capsule.m_radius * capsule.m_radius;
// 始点がカプセルの内側にあるか判定
{
PfxFloat h = fabsf(startPosL[0]);
if(h > capsule.m_halfLen) h = capsule.m_halfLen;
PfxVector3 Px(out.m_variable,0,0);
PfxFloat sqrLen = lengthSqr(startPosL-Px);
if(sqrLen <= radSqr) return false;
}
// カプセルの胴体との交差判定
do {
PfxVector3 P(startPosL);
PfxVector3 D(rayDirL);
P[0] = 0.0f;
D[0] = 0.0f;
PfxFloat a = dot(D,D);
PfxFloat b = dot(P,D);
PfxFloat c = dot(P,P) - radSqr;
PfxFloat d = b * b - a * c;
if(d < 0.0f || fabs(a) < 0.00001f) return false;
PfxFloat tt = ( -b - sqrtf(d) ) / a;
if(tt < 0.0f)
break;
else if(tt > 1.0f)
return false;
if(tt < out.m_variable) {
PfxVector3 cp = startPosL + tt * rayDirL;
if(fabsf(cp[0]) <= capsule.m_halfLen) {
out.m_contactFlag = true;
out.m_variable = tt;
out.m_contactPoint = PfxVector3(transform * PfxPoint3(cp));
out.m_contactNormal = transform.getUpper3x3() * normalize(cp);
out.m_subData.m_type = PfxSubData::NONE;
return true;
}
}
} while(0);
// カプセルの両端にある球体との交差判定
PfxFloat a = dot(rayDirL,rayDirL);
if(fabs(a) < 0.00001f) return false;
do {
PfxVector3 center(capsule.m_halfLen,0.0f,0.0f);
PfxVector3 v = startPosL - center;
PfxFloat b = dot(v,rayDirL);
PfxFloat c = dot(v,v) - radSqr;
PfxFloat d = b * b - a * c;
if(d < 0.0f) break;
PfxFloat tt = ( -b - sqrtf(d) ) / a;
if(tt < 0.0f || tt > 1.0f) break;
if(tt < out.m_variable) {
PfxVector3 cp = startPosL + tt * rayDirL;
out.m_contactFlag = true;
out.m_variable = tt;
out.m_contactPoint = ray.m_startPosition + tt * ray.m_direction;
out.m_contactNormal = transform.getUpper3x3() * normalize(cp-center);
out.m_subData.m_type = PfxSubData::NONE;
return true;
}
} while(0);
{
PfxVector3 center(-capsule.m_halfLen,0.0f,0.0f);
PfxVector3 v = startPosL - center;
PfxFloat b = dot(v,rayDirL);
PfxFloat c = dot(v,v) - radSqr;
PfxFloat d = b * b - a * c;
if(d < 0.0f) return false;
PfxFloat tt = ( -b - sqrtf(d) ) / a;
if(tt < 0.0f || tt > 1.0f) return false;
if(tt < out.m_variable) {
PfxVector3 cp = startPosL + out.m_variable * rayDirL;
out.m_contactFlag = true;
out.m_variable = tt;
out.m_contactPoint = ray.m_startPosition + tt * ray.m_direction;
out.m_contactNormal = transform.getUpper3x3() * normalize(cp-center);
out.m_subData.m_type = PfxSubData::NONE;
return true;
}
}
return false;
}
PfxBool pfxIntersectRayCylinder(const PfxRayInput &ray,PfxRayOutput &out,const PfxCylinder &cylinder,const PfxTransform3 &transform)
{
// レイを円柱のローカル座標へ変換
PfxTransform3 transformCapsule = orthoInverse(transform);
PfxVector3 startPosL = transformCapsule.getUpper3x3() * ray.m_startPosition + transformCapsule.getTranslation();
PfxVector3 rayDirL = transformCapsule.getUpper3x3() * ray.m_direction;
PfxFloat radSqr = cylinder.m_radius * cylinder.m_radius;
// 始点が円柱の内側にあるか判定
{
PfxFloat h = startPosL[0];
if(-cylinder.m_halfLen <= h && h <= cylinder.m_halfLen) {
PfxVector3 Px(h,0,0);
PfxFloat sqrLen = lengthSqr(startPosL-Px);
if(sqrLen <= radSqr) return false;
}
}
// 円柱の胴体との交差判定
do {
PfxVector3 P(startPosL);
PfxVector3 D(rayDirL);
P[0] = 0.0f;
D[0] = 0.0f;
PfxFloat a = dot(D,D);
PfxFloat b = dot(P,D);
PfxFloat c = dot(P,P) - radSqr;
PfxFloat d = b * b - a * c;
if(d < 0.0f) return false; // レイは逸れている
if(pfxAbsf(a) < 0.00001f) break; // レイがX軸に平行
PfxFloat tt = ( -b - sqrtf(d) ) / a;
if(tt < 0.0f || tt > 1.0f) break;
if(tt < out.m_variable) {
PfxVector3 cp = startPosL + tt * rayDirL;
if(pfxAbsf(cp[0]) <= cylinder.m_halfLen) {
out.m_contactFlag = true;
out.m_variable = tt;
out.m_contactPoint = PfxVector3(transform * PfxPoint3(cp));
out.m_contactNormal = transform.getUpper3x3() * normalize(cp);
out.m_subData.m_type = PfxSubData::NONE;
return true;
}
}
} while(0);
// 円柱の両端にある平面との交差判定
{
if(pfxAbsf(rayDirL[0]) < 0.00001f) return false;
PfxFloat t1 = ( cylinder.m_halfLen - startPosL[0] ) / rayDirL[0];
PfxFloat t2 = ( - cylinder.m_halfLen - startPosL[0] ) / rayDirL[0];
PfxFloat tt = SCE_PFX_MIN(t1,t2);
if(tt < 0.0f || tt > 1.0f) return false;
PfxVector3 p = startPosL + tt * rayDirL;
p[0] = 0.0f;
if(lengthSqr(p) < radSqr && tt < out.m_variable) {
PfxVector3 cp = startPosL + tt * rayDirL;
out.m_contactFlag = true;
out.m_variable = tt;
out.m_contactPoint = ray.m_startPosition + tt * ray.m_direction;
out.m_contactNormal = transform.getUpper3x3() * ((cp[0]>0.0f)?PfxVector3(1.0,0.0,0.0):PfxVector3(-1.0,0.0,0.0));
out.m_subData.m_type = PfxSubData::NONE;
return true;
}
}
return false;
}
return about;
}
namespace Feel
{
using namespace vf;
template<int Dim>struct ExactSolution {};
template<>
struct ExactSolution<1>
{
typedef __typeof__( sin( M_PI*Px() ) ) type;
typedef __typeof__( M_PI*M_PI*sin( M_PI*Px() ) ) laplacian_type;
};
template<>
struct ExactSolution<2>
{
typedef __typeof__( sin( M_PI*Px() )*cos( M_PI*Py() ) ) type;
typedef __typeof__( 2*M_PI*M_PI*sin( M_PI*Px() )*cos( M_PI*Py() ) ) laplacian_type;
};
template<>
struct ExactSolution<3>
{
typedef __typeof__( sin( M_PI*Px() )*cos( M_PI*Py() )*cos( M_PI*Pz() ) ) type;
typedef __typeof__( 3*M_PI*M_PI*sin( M_PI*Px() )*cos( M_PI*Py() )*cos( M_PI*Pz() ) ) laplacian_type;
};
