-- FreeFem++ v4.12 (Sat 06 May 2023 07:56:14 PM CEST - git v4.12-72-gb0015903) file : ./periodic3.edp Load: lg_fem lg_mesh lg_mesh3 eigenvalue 1 : load "msh3" 2 : 3 : mesh3 Th3 = cube(10,10,10,[x*2*pi,y*2*pi,z*2*pi]); 4 : 5 : verbosity=10; 6 : fespace Vh3(Th3,P1, periodic=[[1,x,z],[3,x,z],[2,y,z],[4,y,z],[5,x,y],[6,x,y]]); 7 : macro grad3(u) [dx(u),dy(u),dz(u)] ) // 8 : cout << " Vh3 ndof " << Vh3.ndof << endl; 9 : func u3e =(sin(x+1)*sin(y+2)*sin(z+3)); 10 : Vh3 u3,v3,u3h=u3e; 11 : func f3= 3.*u3e; 12 : solve P3(u3,v3) = int3d(Th3)(grad3(u3) [dx(u3),dy(u3),dz(u3)]'*grad3(v3) [dx(v3),dy(v3),dz(v3)]+1e-6*u3*v3) - int3d(Th3)(f3*v3) ; 13 : //plot(u3,u3h,cmm=1); 14 : //plot(u3h,cmm=1); 15 : u3[]-=u3h[]; 16 : cout << " err3 = " << u3[].linfty << endl; 17 : assert(u3[].linfty < 0.07); sizestack + 1024 =4160 ( 3136 ) -- Cube nv=1331 nt=6000 nbe=1200 kind= 6 Nb of pair of periodic conditions (3d) : = 3 dhat: 2 BE::nv: 3 Periodic3 : 1 3 0 Periodic3 : 2 4 6 Periodic3 : 5 6 12 Periodic = 600 600 step=0 Periodic3 : 1 3 0 Periodic3 : 2 4 6 Periodic3 : 5 6 12 --Update: periodic couple label1= 1, n faces= 200; , label2= 3, n BC= 200 --Update: periodic 0 0 6.28319 6.28319 h=0.628319 , coef = 12.7324 / 12800 ~HashTable: Cas moyen : 1 --Update: periodic couple label1= 2, n faces= 200; , label2= 4, n BC= 200 --Update: periodic 0 0 6.28319 6.28319 h=0.628319 , coef = 12.7324 / 12800 ~HashTable: Cas moyen : 1.405 --Update: periodic couple label1= 5, n faces= 200; , label2= 6, n BC= 200 --Update: periodic 0 0 6.28319 6.28319 h=0.628319 , coef = 12.7324 / 12800 ~HashTable: Cas moyen : 1.385 nb equi be : 600 -- BuildDF: iteration in final equivalent 1 nb change 174 -- BuildDF: iteration in final equivalent 3 nb change 4 -- BuildDF: iteration in final equivalent 5 nb change 0 ~HashTable: Cas moyen : 0.120544 ~HashTable: Cas moyen : 0.958333 -- Build Nodes/DF on mesh : n.v. 1331, n. elmt. 6000, n b. elmt. 1200 nb of Nodes 1000 nb of DoF 1000 DFon=1000 -- FESpace: Nb of Nodes 1000 Nb of DoF 1000 Vh3 ndof 1000 -- vector function's bound -0.964086 0.964086 **Warning: set default solver to UMFPACK -- Change of Mesh 0 0x55d78ab83330 Problem(): initmat 1 VF (discontinuous Galerkin) = 0 -- size of Matrix 0 Bytes -- discontinuous Galerkin =0 size of Mat =0 Bytes -- int3d (nQP: 14 ) in Optimized = 1, all -- AssembleLinearForm 1, discontinuous Galerkin =0 binside = 0 -- int 3d (nQP: 14 ) in Optimized = 1, all ** Search solver UMFPACK sym = 0 pos. 0 half 0 ** Find solver UMFPACK ts: 49 sym = 0 pos. 0 half 0 build solver UMFPACK double/int ## SetSolver 0x55d78ab6ac30 0 0x55d78abcc930 UpdateState 1 1 VirtualSolver :: factorize state:0 st= 3 fac_symbolic UMFPACK R: nnz U nnz= 15000 CheckUmfpackStatus 0 fac_numeric UMFPACK R: nnz U nnz= 15000 CheckUmfpackStatus 0 dosolver UMFPACK double/int 1 0 CheckUmfpackStatus 0 UMFPACK V5.7.9 (Oct 20, 2019), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: no. CPU timer: POSIX C clock_getttime ( ) routine. number of rows in matrix A: 1000 number of columns in matrix A: 1000 entries in matrix A: 15000 memory usage reported in: 8-byte Units size of int: 4 bytes size of SuiteSparse_long: 8 bytes size of pointer: 8 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 1000 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 14000 nz on diagonal of matrix S: 1000 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 4.68449e+07 est. nz in L+U (incl. diagonal): 248488 est. largest front (# entries): 104329 est. max nz in any column of L: 323 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 40313 symbolic memory usage (MBytes): 0.3 Symbolic size (Units): 2804 Symbolic size (MBytes): 0 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.53982e+00 maximum sum (abs (rows of A)): 7.53982e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 52007 50003 96% peak size (Units) 1130039 463487 41% final size (Units) 735772 251932 34% Numeric final size (Units) 742321 257981 35% Numeric final size (MBytes) 5.7 2.0 35% peak memory usage (Units) 1147347 480795 42% peak memory usage (MBytes) 8.8 3.7 42% numeric factorization flops 2.68956e+08 4.68427e+07 17% nz in L (incl diagonal) 292067 124742 43% nz in U (incl diagonal) 391867 124742 32% nz in L+U (incl diagonal) 682934 248484 36% largest front (# entries) 306323 104329 34% largest # rows in front 487 323 66% largest # columns in front 629 323 51% initial allocation ratio used: 0.463 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 124742 nz in U (incl diagonal), if none dropped 124742 number of small entries dropped 0 nonzeros on diagonal of U: 1000 min abs. value on diagonal of U: 1.15e-01 max abs. value on diagonal of U: 5.00e-01 estimate of reciprocal of condition number: 2.31e-01 indices in compressed pattern: 8763 numerical values stored in Numeric object: 248488 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 1 numeric factorization wallclock time (sec): 0.69 numeric factorization mflops (wallclock): 68.08 symbolic + numeric wall clock time (sec): 0.69 symbolic + numeric mflops (wall clock): 67.96 solve flops: 1.72590e+06 iterative refinement steps taken: 2 iterative refinement steps attempted: 2 sparse backward error omega1: 2.05e-02 sparse backward error omega2: 0.00e+00 solve wall clock time (sec): 0.00 solve mflops (wall clock time): 1261.77 total symbolic + numeric + solve flops: 4.85686e+07 total symbolic+numeric+solve wall clock time: 0.69 total symbolic+numeric+solve mflops(wallclock) 70.33 -- Solve : min -0.812903 max 0.993395 err3 = 0.152582 current line = 17 Exec error : exec assert -- number :1 ~HashMatrix: Mean collision in hash: 1.24528 0x55d78ab6ac30 rank: 0 matmul 0s destroy mesh30x55d78ab83330 destroy meshS 0 ~GTree the tree NbTreeBox = 644 Nb Vertices = 1331 NbTreeBoxSearch 0 NbVerticesSearch 0 NbSearch 0 ratio: 0 SizeOf QuadTree57696 Exec error : exec assert -- number :1 err code 8 , mpirank 0