Example #1
0
void
Quad10_2D_SUPG :: giveLocalVelocityDofMap(IntArray &map)
{
    map.enumerate(8);
}
Example #2
0
NM_Status
InverseIteration :: solve(SparseMtrx &a, SparseMtrx &b, FloatArray &_eigv, FloatMatrix &_r, double rtol, int nroot)
{
	FILE *outStream;
    if ( a.giveNumberOfColumns() != b.giveNumberOfColumns() ) {
        OOFEM_ERROR("matrices size mismatch");
    }

    SparseLinearSystemNM *solver = GiveClassFactory().createSparseLinSolver(ST_Direct, domain, engngModel);
   
    int nn = a.giveNumberOfColumns();
    int nc = min(2 * nroot, nroot + 8);
    nc = min(nc, nn);

	//// control of diagonal zeroes in mass matrix, to be avoided
	//int i;
	//for (i = 1; i <= nn; i++) {
	//	if (b.at(i, i) == 0) {
	//		b.at(i, i) = 1.0e-12;
	//	}
	//}

    FloatArray w(nc), ww(nc), t;
    std :: vector< FloatArray > z(nc, nn), zz(nc, nn), x(nc, nn);
	outStream = domain->giveEngngModel()->giveOutputStream();

    /*  initial setting  */
#if 0
    ww.add(1.0);
    for ( int j = 0; j < nc; j++ ) {
        z[j].add(1.0);
    }
#else
	{
		FloatArray ad(nn), bd(nn);
		for (int i = 1; i <= nn; i++) {
			ad.at(i) = fabs(a.at(i, i));
			bd.at(i) = fabs(b.at(i, i));
			}
		IntArray order;
		order.enumerate(nn);
		std::sort(order.begin(), order.end(), [&ad, &bd](int a, int b) { return bd.at(a) * ad.at(b) > bd.at(b) * ad.at(a); });
		for (int i = 0; i < nc; i++) {
			x[i].at(order[i]) = 1.0;
			b.times(x[i], z[i]);
			ww.at(i + 1) = z[i].dotProduct(x[i]);
		}
	}
#endif

    int it;
    for ( it = 0; it < nitem; it++ ) {
        /*  copy zz=z  */
        for ( int j = 0; j < nc; j++ ) {
            zz[j] = z[j];
        }

        /*  solve matrix equation K.X = M.X  */
        for ( int j = 0; j < nc; j++ ) {
            solver->solve(a, z[j], x[j]);
        }

        /*  evaluation of Rayleigh quotients  */
        for ( int j = 0; j < nc; j++ ) {
            w.at(j + 1) = zz[j].dotProduct(x[j]);
        }

        for ( int j = 0; j < nc; j++ ) {
            b.times(x[j], z[j]);
        }

        for ( int j = 0; j < nc; j++ ) {
            w.at(j + 1) /= z[j].dotProduct(x[j]);
        }

        /*  check convergence  */
        int ac = 0;
        for ( int j = 1; j <= nc; j++ ) {
            if ( fabs( ww.at(j) - w.at(j) ) <= fabs( w.at(j) * rtol ) ) {
                ac++;
            }

            ww.at(j) = w.at(j);
        }

        //printf ("\n iteration  %d   %d",it,ac);
        //w.printYourself();

        /*  Gramm-Schmidt ortogonalization   */
        for ( int j = 0; j < nc; j++ ) {
            if ( j != 0 ) {
                b.times(x[j], t);
            }

            for ( int ii = 0; ii < j; ii++ ) {
                x[j].add( -x[ii].dotProduct(t), x[ii] );
            }

            b.times(x[j], t);
            x[j].times( 1.0 / sqrt( x[j].dotProduct(t) ) );
        }

        if ( ac > nroot ) {
            break;
        }

        /*  compute new approximation of Z  */
        for ( int j = 0; j < nc; j++ ) {
            b.times(x[j], z[j]);
        }
    }

    // copy results
    IntArray order;
    order.enumerate(w.giveSize());
    std :: sort(order.begin(), order.end(), [&w](int a, int b) { return w.at(a) < w.at(b); });

    _eigv.resize(nroot);
    _r.resize(nn, nroot);
    for ( int i = 1; i <= nroot; i++ ) {
        _eigv.at(i) = w.at(order.at(i));
        _r.setColumn(x[order.at(i) - 1], i);
    }

    if ( it < nitem ) {
		fprintf(outStream, "InverseIteration :: convergence reached in %d iterations\n", it);
    } else {
		fprintf(outStream, "InverseIteration :: convergence not reached after %d iterations\n", it);
    }

    return NM_Success;
}