reduced stiffness matrix improved performance

src/directsolver.jl

@@ -38,7 +38,7 @@ function time_elapsed(timing, what::ASCIIString)
 end
 
 """ Call solver to solve a set of problems. """
-function call(solver::DirectSolver, time::Number=0.0)
+function call(solver::DirectSolver, ::Type{Val{:noreduce}}, time::Number=0.0)
     #@assert length(solver.field_problems) == 1
     info("# of field problems: $(length(solver.field_problems))")
     info("# of boundary problems: $(length(solver.boundary_problems))")
@@ -229,3 +229,204 @@ function call(solver::DirectSolver, time::Number=0.0)
 
 end
 
+
+""" Call solver to solve a set of problems. """
+function call(solver::DirectSolver, time::Number=0.0)
+    info("# of field problems: $(length(solver.field_problems))")
+    info("# of boundary problems: $(length(solver.boundary_problems))")
+    @assert solver.nonlinear_problem == true
+    
+    timing = Dict{ASCIIString, Float64}()
+    tic(timing, "solver")
+    tic(timing, "initialization")
+
+    # check that all problems are "same kind"
+    field_name = get_unknown_field_name(solver.field_problems[1])
+    field_dim = get_unknown_field_dimension(solver.field_problems[1])
+    for field_problem in solver.field_problems
+        get_unknown_field_name(field_problem) == field_name || error("several different fields not supported yet")
+        get_unknown_field_dimension(field_problem) == field_dim || error("several different field dimensions not supported yet")
+    end
+
+    # create initial fields for this increment
+    # i.e., copy last known values as initial guess
+    # for this increment
+
+    for field_problem in solver.field_problems
+        for element in get_elements(field_problem)
+            gdofs = get_gdofs(element, field_dim)
+            if haskey(element, field_name)
+                if !isapprox(last(element[field_name]).time, time)
+                    last_data = copy(last(element[field_name]).data)
+                    push!(element[field_name], time => last_data)
+                end
+            else
+                data = Vector{Float64}[zeros(field_dim) for i in 1:length(element)]
+                element[field_name] = (time => data)
+            end
+        end
+    end
+
+    for boundary_problem in solver.boundary_problems
+        for element in get_elements(boundary_problem)
+            gdofs = get_gdofs(element, field_dim)
+            data = Vector{Float64}[zeros(field_dim) for i in 1:length(element)]
+            if haskey(element, "reaction force")
+                if !isapprox(last(element["reaction force"]).time, time)
+                    push!(element["reaction force"], time => data)
+                end
+            else
+                element["reaction force"] = (time => data)
+            end
+        end
+    end
+
+    toc(timing, "initialization")
+
+    dim = 0
+
+    for iter=1:solver.max_iterations
+        info("Starting iteration $iter")
+        tic(timing, "non-linear iteration")
+
+        mapper = solver.parallel ? pmap : map
+
+        info("Assembling boundary problems...")
+        tic(timing, "boundary assembly")
+        boundary_assembly = sum(mapper((p)->assemble(p, time), solver.boundary_problems))
+        boundary_dofs = unique(boundary_assembly.stiffness_matrix.I)
+        info("# of interface dofs: $(length(boundary_dofs))")
+        toc(timing, "boundary assembly")
+
+        info("Assembling field problems...")
+        dim = 0
+        assemblies = []
+        for (i, problem) in enumerate(solver.field_problems)
+            info("Assembling body $i...")
+            tic(timing, "field assembly")
+            field_assembly = assemble(problem, time)
+            toc(timing, "field assembly")
+            field_dofs = unique(field_assembly.stiffness_matrix.I)
+            info("# of dofs in problem $i: $(length(field_dofs))")
+            info("Eliminating interior dofs for body $i...")
+            dim = maximum([dim, maximum(field_dofs)])
+            tic(timing, "condensate")
+            cfield_assembly = reduce(field_assembly, boundary_dofs)
+            toc(timing, "condensate")
+            push!(assemblies, cfield_assembly)
+        end
+
+        tic(timing, "create sparse matrices")
+        K = spzeros(dim, dim)
+        f = spzeros(dim, 1)
+
+        for (i, assembly) in enumerate(assemblies)
+            resize!(assembly.Kc, dim, dim)
+            resize!(assembly.fc, dim, 1)
+            K += assembly.Kc
+            f += assembly.fc
+        end
+
+        C = sparse(boundary_assembly.stiffness_matrix, dim, dim)
+        g = sparse(boundary_assembly.force_vector, dim, 1)
+        A = [K C'; C spzeros(dim, dim)]
+        b = [f; g]
+        toc(timing, "create sparse matrices")
+
+        info("Solving interface system")
+        tic(timing, "solution of system")
+        nz = sort(unique(rowvals(A)))  # take only non-zero rows
+        sol = zeros(b)
+        sol[nz] = A[nz,nz] \ full(b[nz])
+        toc(timing, "solution of system")
+
+#=
+        try
+        catch
+            dump(round(full(A[nz,nz]), 3))
+            dump(round(full(b[nz]'), 3))
+            for (i, assembly) in enumerate(assemblies)
+                info("assembly $i dump")
+                dump(round(full(assembly.Kc), 3))
+                dump(round(full(assembly.fc), 3)')
+            end
+            info("matrix K")
+            dump(round(full(K), 3))
+            info("interface matrix")
+            dump(round(full(C), 3))
+            info("final assembly to solve:")
+            dump(round(full(A), 3))
+            dump(round(full(b'), 3))
+            info("nonzero dofs: $nz")
+            info("nonzero dofs removed:")
+            dump(round(full(A[nz,nz]), 3))
+            dump(round(full(b[nz]'), 3))
+            detsys = det(A[nz,nz])
+            info("determinant of system: $detsys")
+            error("Solving system failed.")
+        end
+=#
+
+        info("Solved, calculating interior dofs...")
+        tic(timing, "back substitute")
+        for assembly in assemblies
+            length(assembly.interior_dofs) != 0 || continue
+            reconstruct!(assembly, sol)
+        end
+        toc(timing, "back substitute")
+
+        la = sol[dim+1:end]
+        la = vec(full(la))
+        sol = vec(full(sol))
+
+        info("Problem solved. solution norm: $(norm(sol[1:dim]))")
+
+        tic(timing, "update element data")
+        # update elements in field problems
+        for field_problem in solver.field_problems
+            for element in get_elements(field_problem)
+                gdofs = get_gdofs(element, field_dim)
+                local_sol = sol[gdofs]  # incremental data for element
+                local_sol = reshape(local_sol, field_dim, length(element))
+                local_sol = Vector{Float64}[local_sol[:,i] for i=1:length(element)]
+                last(element[field_name]).data += local_sol  # <-- added
+            end
+        end
+
+        # update elements in boundary problems
+        for boundary_problem in solver.boundary_problems
+            for element in get_elements(boundary_problem)
+                gdofs = get_gdofs(element, field_dim)
+                local_sol = la[gdofs]
+                local_sol = reshape(local_sol, field_dim, length(element))
+                local_sol = Vector{Float64}[local_sol[:,i] for i=1:length(element)]
+                last(element["reaction force"]).data = local_sol  # <-- replaced
+            end
+        end
+        toc(timing, "update element data")
+        toc(timing, "non-linear iteration")
+
+        if true
+            info("timing info for non-linear iteration:")
+            info("boundary assembly       : ", time_elapsed(timing, "boundary assembly"))
+            info("field assembly          : ", time_elapsed(timing, "field assembly"))
+            info("reduce stiffness matrix : ", time_elapsed(timing, "condensate"))
+            info("create sparse matrices  : ", time_elapsed(timing, "create sparse matrices"))
+            info("solution of system      : ", time_elapsed(timing, "solution of system"))
+            info("update element data     : ", time_elapsed(timing, "update element data"))
+            info("non-linear iteration    : ", time_elapsed(timing, "non-linear iteration"))
+        end
+
+        if norm(sol[1:dim]) < solver.tol
+            toc(timing, "solver")
+            info("solver finished in ", time_elapsed(timing, "solver"), " seconds.")
+            return (iter, true)
+        end
+
+    end
+
+    info("Warning: did not coverge in $(solver.max_iterations) iterations!")
+    return (solver.max_iterations, false)
+
+end
+