!> `bem_field_solver` の octree 構築・更新とメモリ管理を実装する submodule。 submodule(bem_field_solver) bem_field_solver_tree implicit none contains !> 現在の要素電荷から各ノードの monopole モーメントを再集計する。 module procedure refresh_field_solver integer(i32) :: node_idx, child_k, child_node integer(i32) :: p, idx, p_end integer(i32) :: depth, level_pos, level_start_pos, level_end_pos real(dp) :: q, abs_q, qx, qy, qz, qi if (trim(self%mode) /= 'treecode' .and. trim(self%mode) /= 'fmm') return if (trim(self%mode) == 'fmm') then call refresh_fmm_solver(self, mesh) return end if if (mesh%nelem <= 0_i32) return if (.not. self%tree_ready .or. self%nelem /= mesh%nelem) then self%nelem = mesh%nelem call build_tree_topology(self, mesh) end if if (.not. allocated(self%node_level_start) .or. .not. allocated(self%node_level_nodes)) then call rebuild_source_level_cache(self) end if do depth = self%node_max_depth, 0_i32, -1_i32 level_start_pos = self%node_level_start(depth + 1_i32) level_end_pos = self%node_level_start(depth + 2_i32) - 1_i32 !$omp parallel do default(none) schedule(static) & !$omp shared(self,mesh,level_start_pos,level_end_pos) & !$omp private(level_pos,node_idx,child_k,child_node,p,idx,p_end,q,abs_q,qx,qy,qz,qi) do level_pos = level_start_pos, level_end_pos node_idx = self%node_level_nodes(level_pos) if (self%child_count(node_idx) <= 0_i32) then q = 0.0d0 abs_q = 0.0d0 qx = 0.0d0 qy = 0.0d0 qz = 0.0d0 p_end = self%node_start(node_idx) + self%node_count(node_idx) - 1_i32 do p = self%node_start(node_idx), p_end idx = self%elem_order(p) qi = mesh%q_elem(idx) q = q + qi abs_q = abs_q + abs(qi) qx = qx + qi*mesh%center_x(idx) qy = qy + qi*mesh%center_y(idx) qz = qz + qi*mesh%center_z(idx) end do else q = 0.0d0 abs_q = 0.0d0 qx = 0.0d0 qy = 0.0d0 qz = 0.0d0 do child_k = 1_i32, self%child_count(node_idx) child_node = self%child_idx(child_k, node_idx) q = q + self%node_q(child_node) abs_q = abs_q + self%node_abs_q(child_node) qx = qx + self%node_qx(child_node) qy = qy + self%node_qy(child_node) qz = qz + self%node_qz(child_node) end do end if self%node_q(node_idx) = q self%node_abs_q(node_idx) = abs_q self%node_qx(node_idx) = qx self%node_qy(node_idx) = qy self%node_qz(node_idx) = qz if (abs(q) > tiny(1.0d0)) then self%node_charge_center(1, node_idx) = qx/q self%node_charge_center(2, node_idx) = qy/q self%node_charge_center(3, node_idx) = qz/q else self%node_charge_center(:, node_idx) = self%node_center(:, node_idx) end if end do !$omp end parallel do end do end procedure refresh_field_solver !> 要素重心を octree に再配置して木構造トポロジを構築する。 module procedure build_tree_topology integer(i32) :: i, max_node_guess if (mesh%nelem <= 0_i32) then call reset_tree_storage(self) self%tree_ready = .false. self%nelem = 0_i32 return end if max_node_guess = max(1_i32, 2_i32*mesh%nelem) call ensure_tree_capacity(self, max_node_guess) if (allocated(self%elem_order)) then if (size(self%elem_order) /= mesh%nelem) deallocate (self%elem_order) end if if (.not. allocated(self%elem_order)) allocate (self%elem_order(mesh%nelem)) !$omp parallel do default(none) schedule(static) & !$omp shared(self,mesh) private(i) do i = 1_i32, mesh%nelem self%elem_order(i) = i end do !$omp end parallel do self%nnode = 1_i32 self%node_max_depth = 0_i32 call build_node(self, mesh, 1_i32, 1_i32, mesh%nelem, 0_i32) call rebuild_source_level_cache(self) self%nelem = mesh%nelem self%tree_ready = .true. end procedure build_tree_topology !> 指定区間の要素を1ノードとして登録し、条件を満たせば8分木分割する。 module procedure build_node integer(i32) :: count, p, idx, oct integer(i32) :: child_k, child_node, child_start, child_end integer(i32), allocatable :: counts(:), offsets(:), cursor(:), work(:) real(dp) :: bb_min(3), bb_max(3), span(3), center(3), vertex_radius real(dp) :: split_eps count = end_idx - start_idx + 1_i32 self%node_start(node_idx) = start_idx self%node_count(node_idx) = count self%child_count(node_idx) = 0_i32 self%child_idx(:, node_idx) = 0_i32 self%child_octant(:, node_idx) = 0_i32 self%node_depth(node_idx) = depth self%node_max_depth = max(self%node_max_depth, depth) idx = self%elem_order(start_idx) bb_min = [mesh%center_x(idx), mesh%center_y(idx), mesh%center_z(idx)] bb_max = bb_min do p = start_idx + 1_i32, end_idx idx = self%elem_order(p) bb_min(1) = min(bb_min(1), mesh%center_x(idx)) bb_min(2) = min(bb_min(2), mesh%center_y(idx)) bb_min(3) = min(bb_min(3), mesh%center_z(idx)) bb_max(1) = max(bb_max(1), mesh%center_x(idx)) bb_max(2) = max(bb_max(2), mesh%center_y(idx)) bb_max(3) = max(bb_max(3), mesh%center_z(idx)) end do span = bb_max - bb_min center = 0.5d0*(bb_max + bb_min) self%node_center(:, node_idx) = center self%node_half_size(:, node_idx) = 0.5d0*span self%node_radius(node_idx) = sqrt(sum(self%node_half_size(:, node_idx)*self%node_half_size(:, node_idx))) do p = start_idx, end_idx idx = self%elem_order(p) vertex_radius = sqrt(sum((mesh%v0(:, idx) - center)**2)) self%node_radius(node_idx) = max(self%node_radius(node_idx), vertex_radius) vertex_radius = sqrt(sum((mesh%v1(:, idx) - center)**2)) self%node_radius(node_idx) = max(self%node_radius(node_idx), vertex_radius) vertex_radius = sqrt(sum((mesh%v2(:, idx) - center)**2)) self%node_radius(node_idx) = max(self%node_radius(node_idx), vertex_radius) end do if (count <= self%leaf_max) return split_eps = 1.0d-12*max(1.0d0, maxval(abs(center))) if (maxval(span) <= split_eps) return allocate (counts(8), offsets(8), cursor(8), work(count)) counts = 0_i32 do p = start_idx, end_idx idx = self%elem_order(p) oct = octant_index(mesh%center_x(idx), mesh%center_y(idx), mesh%center_z(idx), center) counts(oct) = counts(oct) + 1_i32 end do if (maxval(counts) == count) then deallocate (counts, offsets, cursor, work) return end if offsets(1) = 1_i32 do oct = 2, 8 offsets(oct) = offsets(oct - 1) + counts(oct - 1) end do cursor = offsets do p = start_idx, end_idx idx = self%elem_order(p) oct = octant_index(mesh%center_x(idx), mesh%center_y(idx), mesh%center_z(idx), center) work(cursor(oct)) = idx cursor(oct) = cursor(oct) + 1_i32 end do self%elem_order(start_idx:end_idx) = work child_k = 0_i32 child_start = start_idx do oct = 1, 8 if (counts(oct) <= 0_i32) cycle child_end = child_start + counts(oct) - 1_i32 self%nnode = self%nnode + 1_i32 if (self%nnode > self%max_node) error stop 'field solver tree capacity exceeded.' child_node = self%nnode child_k = child_k + 1_i32 self%child_idx(child_k, node_idx) = child_node self%child_octant(child_k, node_idx) = oct call build_node(self, mesh, child_node, child_start, child_end, depth + 1_i32) child_start = child_end + 1_i32 end do self%child_count(node_idx) = child_k deallocate (counts, offsets, cursor, work) end procedure build_node !> ノード中心に対する座標の相対位置から octant インデックスを返す。 module procedure octant_index oct = 1_i32 if (x >= center(1)) oct = oct + 1_i32 if (y >= center(2)) oct = oct + 2_i32 if (z >= center(3)) oct = oct + 4_i32 end procedure octant_index !> 必要ノード数に合わせて木配列を確保し、利用領域をゼロ初期化する。 module procedure ensure_tree_capacity if (self%max_node == max_node_needed .and. allocated(self%node_start)) then self%node_start = 0_i32 self%node_count = 0_i32 self%child_count = 0_i32 self%child_idx = 0_i32 self%child_octant = 0_i32 self%node_depth = 0_i32 self%node_max_depth = 0_i32 self%node_center = 0.0d0 self%node_half_size = 0.0d0 self%node_radius = 0.0d0 self%node_q = 0.0d0 self%node_abs_q = 0.0d0 self%node_qx = 0.0d0 self%node_qy = 0.0d0 self%node_qz = 0.0d0 self%node_charge_center = 0.0d0 return end if call reset_tree_storage(self) self%max_node = max_node_needed allocate (self%node_start(self%max_node), self%node_count(self%max_node)) allocate (self%child_count(self%max_node), self%child_idx(8, self%max_node), self%child_octant(8, self%max_node)) allocate (self%node_depth(self%max_node)) allocate (self%node_center(3, self%max_node), self%node_half_size(3, self%max_node)) allocate (self%node_radius(self%max_node)) allocate (self%node_q(self%max_node), self%node_abs_q(self%max_node)) allocate (self%node_qx(self%max_node), self%node_qy(self%max_node), self%node_qz(self%max_node)) allocate (self%node_charge_center(3, self%max_node)) self%node_start = 0_i32 self%node_count = 0_i32 self%child_count = 0_i32 self%child_idx = 0_i32 self%child_octant = 0_i32 self%node_depth = 0_i32 self%node_max_depth = 0_i32 self%node_center = 0.0d0 self%node_half_size = 0.0d0 self%node_radius = 0.0d0 self%node_q = 0.0d0 self%node_abs_q = 0.0d0 self%node_qx = 0.0d0 self%node_qy = 0.0d0 self%node_qz = 0.0d0 self%node_charge_center = 0.0d0 end procedure ensure_tree_capacity module procedure rebuild_source_level_cache integer(i32) :: node_idx, depth integer(i32), allocatable :: depth_count(:), cursor(:) if (allocated(self%node_level_start)) deallocate (self%node_level_start) if (allocated(self%node_level_nodes)) deallocate (self%node_level_nodes) if (self%nnode <= 0_i32) return allocate (depth_count(self%node_max_depth + 1_i32), cursor(self%node_max_depth + 1_i32)) depth_count = 0_i32 do node_idx = 1_i32, self%nnode depth_count(self%node_depth(node_idx) + 1_i32) = depth_count(self%node_depth(node_idx) + 1_i32) + 1_i32 end do allocate (self%node_level_start(self%node_max_depth + 2_i32), self%node_level_nodes(self%nnode)) self%node_level_start(1) = 1_i32 do depth = 0_i32, self%node_max_depth self%node_level_start(depth + 2_i32) = self%node_level_start(depth + 1_i32) + depth_count(depth + 1_i32) end do cursor = self%node_level_start(1:self%node_max_depth + 1_i32) do node_idx = 1_i32, self%nnode depth = self%node_depth(node_idx) self%node_level_nodes(cursor(depth + 1_i32)) = node_idx cursor(depth + 1_i32) = cursor(depth + 1_i32) + 1_i32 end do deallocate (depth_count, cursor) end procedure rebuild_source_level_cache !> treecode で使う作業配列を解放し、ノード状態を未初期化に戻す。 module procedure reset_tree_storage if (allocated(self%elem_order)) deallocate (self%elem_order) if (allocated(self%node_start)) deallocate (self%node_start) if (allocated(self%node_count)) deallocate (self%node_count) if (allocated(self%child_count)) deallocate (self%child_count) if (allocated(self%child_idx)) deallocate (self%child_idx) if (allocated(self%child_octant)) deallocate (self%child_octant) if (allocated(self%node_depth)) deallocate (self%node_depth) if (allocated(self%node_level_start)) deallocate (self%node_level_start) if (allocated(self%node_level_nodes)) deallocate (self%node_level_nodes) if (allocated(self%node_center)) deallocate (self%node_center) if (allocated(self%node_half_size)) deallocate (self%node_half_size) if (allocated(self%node_radius)) deallocate (self%node_radius) if (allocated(self%node_q)) deallocate (self%node_q) if (allocated(self%node_abs_q)) deallocate (self%node_abs_q) if (allocated(self%node_qx)) deallocate (self%node_qx) if (allocated(self%node_qy)) deallocate (self%node_qy) if (allocated(self%node_qz)) deallocate (self%node_qz) if (allocated(self%node_charge_center)) deallocate (self%node_charge_center) self%nnode = 0_i32 self%max_node = 0_i32 self%node_max_depth = 0_i32 self%tree_ready = .false. self%nelem = 0_i32 end procedure reset_tree_storage end submodule bem_field_solver_tree