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89 lines
2.9 KiB
89 lines
2.9 KiB
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-11-27 15:21:49
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% @LastEditTime: 2021-12-06 20:12:34
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% could be arbitrary version without considering the length?
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% NOTE: the bdofs must CONFORMS to phi
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% bdofs order of phi: boundary dofs on each edge
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% Three situations:
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% 1. fine boundary nodes >= 2 on this edge, phi as usual
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% 2. fine boundary node = 1 on this edge, phi with 1 contro node
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% 3. fine boundary node = 0 on this edge, phi = eye(4)
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%--------------------------
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function phi_cell = parametric_B_cvt(nbnodes_cell, nbridge_each)
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ncvt = size(nbnodes_cell, 1);
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phi_cell = cell(ncvt,1);
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% figure;
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B2 = simple_quad_Bezier(3);
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for ele = 1 : ncvt
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nbele = nbnodes_cell{ele} - 1;
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nedges = size(nbele, 1);
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ncbn = 1;
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nbdofs = 1;
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standard_nedges = length(find(nbele>2));
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ncbn_1v = standard_nedges * ((nbridge_each+1) * 2 + nbridge_each) + nedges;
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ncbn_1v = ncbn_1v + sum(nbele(nbele <=2) - 1); % for situations 2 & 3
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phi_1v = zeros(sum(nbele)*2, ncbn_1v * 2);
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for edge = 1 : nedges
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nb_edge = nbele(edge);
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% three situations
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if nb_edge > 2
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% 1. fine boundary nodes >= 2 on this edge, phi as usual
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[phi_1b, seg_num] = bezier_one_edge(nb_edge, nbridge_each);
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ncbn_1b = seg_num * 2 + nbridge_each + 2;
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elseif nb_edge == 2
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% 2. fine boundary node = 1 on this edge, phi with 1 contro node
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% linear interpolation
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phi_1b = B2;
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ncbn_1b = 3;
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else
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% 3. fine boundary node = 0 on this edge, phi = ones(2,2)
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phi_1b = eye(4);
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ncbn_1b = 2;
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end
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% to remove the adjoint corner_node
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if edge == nedges
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phi_1v(nbdofs : nbdofs + nb_edge*2 -1, ncbn : ncbn + (ncbn_1b-1)*2 - 1) = phi_1b(1:end-2, 1:end-2);
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phi_1v(nbdofs : nbdofs + nb_edge*2 -1, 1:2) = phi_1b(1:end-2, end-1:end);
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else
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phi_1v(nbdofs : nbdofs + (nb_edge+1)*2 -1, ncbn : ncbn + ncbn_1b*2 - 1) = phi_1b;
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end
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% to remove the adjoint corner_node
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ncbn = ncbn + (ncbn_1b-1) * 2;
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nbdofs = nbdofs + nb_edge * 2;
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end
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phi_cell{ele} = phi_1v;
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end
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end
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function B2 = simple_quad_Bezier(nodes_num)
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B = zeros(2, 6, nodes_num);
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for i = 0 : nodes_num-1
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t = i / (nodes_num-1); % project to [0,1]
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B(:, :, i+1) = Bezier_matrix(t);
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end
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B1 = permute(B, [2,1,3]); % [6, 2, x+1]
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B2 = reshape(B1, 6, [])'; % [2(x+1), 6]
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end
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function B = Bezier_matrix(t)
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b = [1, t, t^2] * [1, 0,0;
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-2,2,0;
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1,-2,1]; % 1,3
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I = eye(2, 2);
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B = kron(b, I); % 2,6
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end
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