From: Jaeryun Yim Date: Thu, 28 Jan 2016 09:08:06 +0000 (+0900) Subject: Add the definition of the face value functions for the P1 nonconforming nonparametric... X-Git-Tag: v8.5.0-rc1~624^2~35 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=5cc38276aa2e5037ae8fd972d23afdc2e943f6ea;p=dealii.git Add the definition of the face value functions for the P1 nonconforming nonparametric element. the definition of 'fill_fe_face_values' & 'fill_fe_subface_values' --- diff --git a/source/fe/fe_p1nc.cc b/source/fe/fe_p1nc.cc index 66d058205a..3cc799604a 100644 --- a/source/fe/fe_p1nc.cc +++ b/source/fe/fe_p1nc.cc @@ -602,7 +602,113 @@ FE_P1NCNonparametric::fill_fe_face_values (const Triangulation<2,2>::cell_iterat const InternalDataBase &fe_internal, dealii::internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const -{} +{ + const UpdateFlags flags(fe_internal.update_each) ; + + const unsigned int n_q_points = mapping_data.quadrature_points.size(); + + std::vector values(flags & update_values ? this->dofs_per_cell : 0); + std::vector > grads(flags & update_gradients ? this->dofs_per_cell : 0); + + + + // edge midpoints + std::vector > mpt(4) ; + + mpt[0](0) = (cell->vertex(0)(0) + cell->vertex(2)(0))/2.0 ; + mpt[0](1) = (cell->vertex(0)(1) + cell->vertex(2)(1))/2.0 ; + + mpt[1](0) = (cell->vertex(1)(0) + cell->vertex(3)(0))/2.0 ; + mpt[1](1) = (cell->vertex(1)(1) + cell->vertex(3)(1))/2.0 ; + + mpt[2](0) = (cell->vertex(0)(0) + cell->vertex(1)(0))/2.0 ; + mpt[2](1) = (cell->vertex(0)(1) + cell->vertex(1)(1))/2.0 ; + + mpt[3](0) = (cell->vertex(2)(0) + cell->vertex(3)(0))/2.0 ; + mpt[3](1) = (cell->vertex(2)(1) + cell->vertex(3)(1))/2.0 ; + + // center point + Point<2> cpt ; + cpt(0) = (mpt[0](0) + mpt[1](0) + mpt[2](0) + mpt[3](0))/4.0 ; + cpt(1) = (mpt[0](1) + mpt[1](1) + mpt[2](1) + mpt[3](1))/4.0 ; + + + // basis functions with a half value: phi(x,y) = ax + by + c + std::vector a(4), b(4), c(4) ; + double det ; + + det = (mpt[0](0)-mpt[1](0))*(mpt[2](1)-mpt[3](1)) - (mpt[2](0)-mpt[3](0))*(mpt[0](1)-mpt[1](1)) ; + + a[0] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ; + a[1] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ; + a[2] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ; + a[3] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ; + + b[0] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ; + b[1] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ; + b[2] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ; + b[3] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ; + + c[0] = 0.25 - cpt(0)*a[0] - cpt(1)*b[0] ; + c[1] = 0.25 - cpt(0)*a[1] - cpt(1)*b[1] ; + c[2] = 0.25 - cpt(0)*a[2] - cpt(1)*b[2] ; + c[3] = 0.25 - cpt(0)*a[3] - cpt(1)*b[3] ; + + + + // compute basis functions + if (flags & (update_values | update_gradients)) + for (unsigned int i=0; idofs_per_cell; ++k) + { + if (flags & update_values) + { + values[k] = a[k]*mapping_data.quadrature_points[i](0) + b[k]*mapping_data.quadrature_points[i](1) + c[k] ; + output_data.shape_values[k][i] = values[k]; + } + + if (flags & update_gradients) + { + grads[k][0] = a[k] ; + grads[k][1] = b[k] ; + output_data.shape_gradients[k][i] = grads[k]; + } + } + + } + + // When this function is called for computation of facial jump residual, + // MappingRelatedData does not work properly. + // In this case, the quadrature points on the real cell is computed in manual sense, using 'mapping' and 'quadrature'. + // This is a temporary solution. It needs to be fixed fundamentally. + if (n_q_points==0) + { + Quadrature<2> cellquadrature = QProjector<2>::project_to_face(quadrature, face_no) ; + for(unsigned int i=0;idofs_per_cell; ++k) + { + if (flags & update_values) + { + Point<2> realquadrature ; + + realquadrature = mapping.transform_unit_to_real_cell(cell, cellquadrature.point(i)) ; + values[k] = a[k]*realquadrature(0) + b[k]*realquadrature(1) + c[k] ; + output_data.shape_values[k][i] = values[k]; + } + + if (flags & update_gradients) + { + grads[k][0] = a[k] ; + grads[k][1] = b[k] ; + output_data.shape_gradients[k][i] = grads[k]; + } + + } + + } + +} @@ -620,7 +726,112 @@ FE_P1NCNonparametric::fill_fe_subface_values (const Triangulation<2,2>::cell_ite const InternalDataBase &fe_internal, dealii::internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const -{} +{ + const UpdateFlags flags(fe_internal.update_each) ; + + const unsigned int n_q_points = mapping_data.quadrature_points.size(); + + std::vector values(flags & update_values ? this->dofs_per_cell : 0); + std::vector > grads(flags & update_gradients ? this->dofs_per_cell : 0); + + + + // edge midpoints + std::vector > mpt(4) ; + + mpt[0](0) = (cell->vertex(0)(0) + cell->vertex(2)(0))/2.0 ; + mpt[0](1) = (cell->vertex(0)(1) + cell->vertex(2)(1))/2.0 ; + + mpt[1](0) = (cell->vertex(1)(0) + cell->vertex(3)(0))/2.0 ; + mpt[1](1) = (cell->vertex(1)(1) + cell->vertex(3)(1))/2.0 ; + + mpt[2](0) = (cell->vertex(0)(0) + cell->vertex(1)(0))/2.0 ; + mpt[2](1) = (cell->vertex(0)(1) + cell->vertex(1)(1))/2.0 ; + + mpt[3](0) = (cell->vertex(2)(0) + cell->vertex(3)(0))/2.0 ; + mpt[3](1) = (cell->vertex(2)(1) + cell->vertex(3)(1))/2.0 ; + + // center point + Point<2> cpt ; + cpt(0) = (mpt[0](0) + mpt[1](0) + mpt[2](0) + mpt[3](0))/4.0 ; + cpt(1) = (mpt[0](1) + mpt[1](1) + mpt[2](1) + mpt[3](1))/4.0 ; + + + // basis functions with a half value: phi(x,y) = ax + by + c + std::vector a(4), b(4), c(4) ; + double det ; + + det = (mpt[0](0)-mpt[1](0))*(mpt[2](1)-mpt[3](1)) - (mpt[2](0)-mpt[3](0))*(mpt[0](1)-mpt[1](1)) ; + + a[0] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ; + a[1] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ; + a[2] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ; + a[3] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ; + + b[0] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ; + b[1] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ; + b[2] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ; + b[3] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ; + + c[0] = 0.25 - cpt(0)*a[0] - cpt(1)*b[0] ; + c[1] = 0.25 - cpt(0)*a[1] - cpt(1)*b[1] ; + c[2] = 0.25 - cpt(0)*a[2] - cpt(1)*b[2] ; + c[3] = 0.25 - cpt(0)*a[3] - cpt(1)*b[3] ; + + + + // compute basis functions + if (flags & (update_values | update_gradients)) + for (unsigned int i=0; idofs_per_cell; ++k) + { + if (flags & update_values) + { + values[k] = a[k]*mapping_data.quadrature_points[i](0) + b[k]*mapping_data.quadrature_points[i](1) + c[k] ; + output_data.shape_values[k][i] = values[k]; + } + + if (flags & update_gradients) + { + grads[k][0] = a[k] ; + grads[k][1] = b[k] ; + output_data.shape_gradients[k][i] = grads[k]; + } + } + + } + + // When this function is called for computation of facial jump residual, + // MappingRelatedData does not work properly. + // In this case, the quadrature points on the real cell is computed in manual sense, using 'mapping' and 'quadrature'. + // This is a temporary solution. It needs to be fixed fundamentally. + if (n_q_points==0) + { + Quadrature<2> cellquadrature = QProjector<2>::project_to_subface(quadrature, face_no, sub_no) ; + for(unsigned int i=0;idofs_per_cell; ++k) + { + if (flags & update_values) + { + Point<2> realquadrature ; + + realquadrature = mapping.transform_unit_to_real_cell(cell, cellquadrature.point(i)) ; + values[k] = a[k]*realquadrature(0) + b[k]*realquadrature(1) + c[k] ; + output_data.shape_values[k][i] = values[k]; + } + + if (flags & update_gradients) + { + grads[k][0] = a[k] ; + grads[k][1] = b[k] ; + output_data.shape_gradients[k][i] = grads[k]; + } + + } + + } +}