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PLTMG 13.0β Quick Reference Guide

Randolph E. Bank
Department of Mathematics
University of California at San Diego
La Jolla, California 92093-0112






Copyright (c) 2018 by the author
This software is made available for research and instructional use only. You may copy and use this software without charge for these non-commercial purposes, provided that the copyright notice and associated text is reproduced on all copies. For all other uses (including distribution of modified versions), please contact the author.
This software is being provided äs is", without any expressed or implied warranty. In particular, the author does not make any representation or warranty of any kind concerning the fitness of this software for any particular purpose.
PLTMG development was supported by the National Science Foundation under grants DMS-1318480, DMS-1345103, and MRI-0821816.
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Chapter 1
Data Structures

ITNODE Array Definitions


ITNODE for triangulation
array entry definition
ITNODE(1,I) first vertex number
ITNODE(2,I) second vertex number
ITNODE(3,I) third vertex number
ITNODE(4,I) reserved for parallel processing
ITNODE(5,I) element label
ITNODE for skeleton
array entry definition
ITNODE(1,I) first vertex number
ITNODE(2,I) first edge number
ITNODE(3,I) congruent region number
ITNODE(4,I) reserved for parallel processing
ITNODE(5,I) region label

IBNDRY Array Definitions


IBNDRY Array Definition
array entry definition
IBNDRY(1,I) first endpoint number
IBNDRY(2,I) second endpoint number
IBNDRY(3,I) curved edge switch
IBNDRY(4,I) edge type
IBNDRY(5,I) reserved for parallel processing
IBNDRY(6,I) reserved for parallel processing
IBNDRY(7,I) edge label
Curved Edge Types
IBNDRY(3,I) curved edge type
0 Straight edge
1 Curved edge - circular arc
−K Curved edge - parametric
Edge Type Definitions
IBNDRY(4,I) edge type
2 Dirichlet boundary
1 natural boundary
0 internal
−Klinked with edge K
3, 4, 5 reserved for parallel processing

SF Array Definitions


SF for circular arc
array entry definition
SF(1,I) center coordinate xc
SF(2,I) center coordinate yc
SF for parametric curve
array entry definition
SF(1,I) parametric coordinate s1
SF(2,I) parametric coordinate s2

ITDOF Array Definitions


array entry definition
ITDOF(1,I) degree of freedom for vertex ν1
ITDOF(2,I) degree of freedom for vertex ν2
ITDOF(3,I) degree of freedom for vertex ν3
ITDOF(4,I) ± first degree of freedom for edge ϵ1
ITDOF(5,I) ± first degree of freedom for edge ϵ2
ITDOF(6,I) ± first degree of freedom for edge ϵ3
ITDOF(7,I) first interior degree of freedom for element tI
ITDOF(8,I) polynomial degrees for element tI

GF Array Definitions


problem 1 2 3 4 5 6 7
simple pde u (ud) (ω)
obstacle problem u (ω)
continuation problem u u0 · u · u0 ψr ψl (ω)
parameter identification u v uλ (ω)
distributed control u v λ (ω)

IPATH Array Definitions


array entry root root/leaf internal leaf
IPATH(1,I)neighbor neighbor neighbor neighbor
IPATH(2,I)child -edge child -edge
IPATH(3,I)vertex 1 vertex 1
IPATH(4,I)vertex 2 vertex 2
IPATH(5,I)± edge ± edge
IPATH(6,I)degree degree

Reset Window Commands


Parameters associated with n command
Name Alias Type Value
vname n short maximum of 6 characters
alias a short maximum of 2 characters
vtype t short i (int), r (real), s (short), l (long), f (file)
index i int pointer to IU, RU, SU
Parameters associated with s command
Name Alias Type Value
vname n short variable name
value v - depends on vname
label l long label associated with value in radio buttons
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Chapter 2
Coefficient Functions


VALUES Array for A1XY, A2XY, FXY, P1XY, P2XY


pointer indexVALUES(·)
K0=1 K0 f
KU=2 KU fu
KX=3 KX fux
KY=4 KY fuy
KL=5 KL+J−1 fλJ
1 ≤ J ≤ NRL

VALUES Array for GNXY


pointer indexVALUES(·)
K0=1 K0 g
KU=2 KU gu
KL=3 KL+J−1 gλJ
1 ≤ J ≤ NRL

VALUES Array for GDXY


pointer indexVALUES(·)
K0=1 K0 g
KL=2 KL+J−1gλJ
KLB=2+NRL KLB+J−1u, λJ
KUB=2+2 NRL KUB+J−1―u, ―λJ
KIC=2+3 NRL KIC u0
KIM=3+3 NRL KIM v0
KIL=4+3 NRLKIL+J−1 λ0,J
1 ≤ J ≤ NRL

VALUES Array for SXY


pointer indexVALUES(1,·)VALUES(2,·)
J0=1 J0 qK rK
JS=2 JS qK,s rK,s
JL=3 JL+J−1 qK,λJ rK,λJ
1 ≤ J ≤ NRL

VALUES Array for QXY


K0 1 alternate scalar function for TRIPLT
KF1 2 first component of vector function for TRIPLT
KF2 3 second component of vector function for TRIPLT
KAD 4 alternate function for adaptive algorithms in TRIGEN
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Chapter 3
IP Array

The parameters marked "u" should be supplied by the user.
IIP(I)udefinition
1 NTF unumber of triangles / regions
2 NVF unumber of vertices
3 NBF unumber of edges
4 NDF unumber of degrees of freedom
5 IFIRSTuinitialization switch
6 IPROB uproblem type
7 ITASK uproblem task
8 ISPD usymmetric / nonsymmetric switch
9 METHODupreconditioner options
10 MXCG umaximum conjugate gradient iterations
11 MXNWTTumaximum damped Newton iterations
12 ISING uswitch for singular Neumann problem
13 NRL unumber of parameters λ
17 IRTYPEurefinement / coarsening options
18 MXORD umaximum polynomial degree
19 IERRSWuerror recovery switch
20 IADAPTumesh generation option switch
21 IREFN uuniform refinement control
22 NDTRGTutarget value for number of vertices
23 NOCHNGuPLTMG-TRIGEN communication flag
24 MFLAG uparallel error flag
25 IFLAG error flag
27 NEWNTFnumber of elements owned by processor
28 NEWNVFnumber of vertices owned by processor
29 NEWNBFnumber of edges owned by processor
30 NEWNDFnumber of degrees of freedom owned by processor
31 NVV number of interface vertices
32 NBB number of interface edges
33 NDD number of interface degrees of freedom
34 NVI number of coarse interface vertices
35 NBI number of coarse interface edges
36 NDI number of coarse degrees of freedom
37 NTG global number of elements
38 NVG global number of vertices
39 NBG global number of edges
40 NDG global number of degrees of freedom
41 IUSRSWuUSRCMD switch
42 MODE uATEST mode switch
43 WEBPRTucommunications socket for WEBGUI
47 MPIRGNuregion for file read/write and graphics
48 MPISW uMPI switch
49 NPROC number of processes
50 IRGN individual process number
51 MXCOLRumaximum number of colors
52 IFUN ualternate function switch for TRIPLT
53 INPLSWualternate graph switch for INPLT
54 IGRSW ualternate graph switch for GPHPLT
55 NCON unumber of contours
56 ICONT ucontinuity switch
57 ISCALEuscale option switch
58 LINES uline drawing option switch
59 NUMBRSunumbering option switch
60 NX u
61 NY u(NX,NY,NZ)
62 NZ uis the viewing perspective for TRIPLT
63 MX u
64 MY u(MX,MY,MZ)
65 MZ uis the viewing perspective for GPHPLT
66 ICRSN ugraphics coarsening switch
67 ITRGT utarget size of graphics mesh
68 IDEVCEugraphics device switch
69 FPANE uWEBGUI canvas for TRIPLT
70 GPANE uWEBGUI canvas for GPHPLT
71 JPANE uWEBGUI canvas for INPLT
73 MXLABL maximum label for MPI interface edges
74 NVDD total number of interface vertices
75 LIPATHlength of IPATH array
76 NEF number of error functions
77 NGF number of grid functions
78 NDL order of error recovery systems
79 IEVALSnumber of function evaluations on last call
80 ITNUM number of Newton iterations on last call
82 MAXPTHunumber of columns in the array IPATH
83 MAXT unumber of columns in the array ITNODE
84 MAXV ulength of the arrays VX and VY
85 MAXD ulength of grid function array GF
86 MAXB unumber of columns in the array IBNDRY
90 NDF order of the linear system
91 NB number of blocks in the linear system
92 LENJA length of JA array
93 LENAD length of diagonal part A array
94 LENAOD length of upper / lower triangular A array
95 LENJU maximum length of JU array
96 LENUOD maximum length of upper / lower triangular U array
97 LENJU0 length of JU array
98 LENU0 length of U array
99 LENJA0 length of JA for HB decomposition
100 LENJUC length of JU for HB decomposition
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Chapter 4
RP Array

The parameters marked "u" should be supplied by the user.
IRP(I)udefinition
1 RLTRGT utarget value for λ
2 RTRGT utarget value for ρ(u,λ)
3 RMTRGT utarget value for μ
4 DTOL udrop tolerance for incomplete factorization
6 SMIN ulower limit for contour colors
7 SMAX uupper limit for contour colors
8 RMAG uwindow magnification factor
9 CENX u(CENX,CENY) are the window center coordinates
10 CENY u
12HMAX uapproximate largest element size
13GRADE ulargest growth factor for adjacent elements
14HMIN uapproximate smallest edge length
16 XMIN
17 XMAX Ω ⊂ (XMIN,XMAX)×(YMIN,YMAX)
18 YMIN
19 YMAX
21 RL current value of λh
22 R current value of ρ(uh,λh)=ρh
23 RLDOT current value of · λh
24 RDOT current value of · ρh
25 SVAL current value of smallest singular value
26 RLSTRTstarting value for λh
27 RSTRT starting value for ρ(uh,λh)
31 RL0 previous value of λh
32 R0 previous value of ρ(uh,λh)=ρh
33 RL0DOTprevious value of · λh
34 R0DOT previous value of · ρh
35 SVAL0 previous value of smallest singular value
37 ENORM1estimate for || u−uh ||H1(Ω)
38 UNORM1the norm || uh ||H1(Ω)
39 ENORM2estimate for || u−uh ||L2(Ω)
40 UNORM2the norm || uh ||L2(Ω)
41 RELERPrelative size of solution error || eh ||H1(ΩI)/|| uh ||H1(ΩI)
42 EAVE2arithmetic average of || eh ||H1(t)2
52 STEP damping step s for Newton's method
53 RELER0relative size of solution error || eh ||H1(Ω)/|| uh ||H1(Ω)
54 RELERRrelative size of Newton update || δU ||/|| U ||
55 ANORM maximum diagonal entry in Jacobian matrix
56 RELRESthe relative residual || Gk ||/|| G0 ||
57 BRATIOthe relative residual || Gk ||/|| Gk−1 ||
58 DNEW the discrete inner product −〈GuδU,G〉
59 BNORM0 scaling factor || G0 ||
60 BMNRM0 scaling factor for ρ
63 RMU current value of interior point parameter μ
64 REG4 internal regularization parameter for IPROB=4
65 REG5 internal regularization parameter for IPROB=5
67 SCLEQNcurrent value of scalar equation N−σ
68 SCALE scaling factor for scalar equation
69 THETAL(2−θ)· λh in scalar equation
70 THETARθ· ρh in scalar equation
71 SIGMA the step σ for scalar equation
72 DELTA Newton update for λh
73 DRDRL the value of ∂ρ/∂λ
74 SEQDOTthe value of · N
76 QUAL target element quality
77 ANGMN target minimum angle
78 DIAM approximate diameter of Ω
79 BEST value of TRIGEN quality function
80 AREA area of Ω
82 N0 degrees of freedom for region ΩI
83 E0 error for region ΩI
84 NF global degrees of freedom
85 EF global error
91 RL1value of λ1
92 RL2value of λ2
93 RL3value of λ3
94 RL4value of λ4
95 RL5value of λ5
96 RL6value of λ6
97 RL7value of λ7
98 RL8value of λ8
99 RL9value of λ9
100RL10value of λ10
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Chapter 5
SP Array

The parameters marked "u" should be supplied by the user.
ISP(I)udefinition
1 ITITLEutitle for INPLT
2 FTITLEutitle for TRIPLT
3 GTITLEutitle for GPHPLT
4 LOGOutitle for web browser tab
5 GRFILEufile for hard copy graphics output
6 RWFILEusave file for read/write commands
7 JRFILEuread file for journal command
8 JWFILEwrite file for journal command
9 BFILE uoutput file
10 JTFILEtemporary file for journal command
11 IOMSG error message string
12 CMD current command string
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Chapter 6
The Parameter IFLAG

IFLAG general return codes
0 normal return
25 wrong input data structure
IFLAG PLTMG and TRIGEN errors
1 zero pivot in sparse factorization
2 Newton method line search failed
6 illegal problem type
7 continuation procedure failed
10 multigraph iteration failed to converge
11 Newton (Newton/DD) iteration failed to converge
24 Error on one or more MPI processes
48 MPI was off for a command needing MPI
49 NPROC > NTF in load balance
71 no interface unknowns in DD solver
72 IPATH array not created
IFLAG storage errors
82 storage exhausted in array IPATH
83 storage exhausted in arrays ITNODE and ITDOF
84 storage exhausted in arrays VX and VY
85 storage exhausted in array GF
86 storage exhausted in arrays IBNDRY and SF
IFLAG data errors for triangulation
−31 illegal ITNODE(K,*) K=1,2,3
−32 overlapping triangles in ITNODE
IFLAG data errors for triangulation and skeleton
−40 illegal value for NVF, NTF, or NBF
−41 illegal IBNDRY(K,*) K=1,2
−42 illegal IBNDRY(3,*)
−43 illegal IBNDRY(4,*)
−44 incorrect circle center coordinates
−45 arc greater than π/2 in length
−46 error in linked edges
−47 boundary vertex without two boundary edges
−48 ITNODE and IBNDRY are not consistent
IFLAG data errors for skeleton
−51 illegal ITNODE(1,*)
−52 illegal ITNODE(2,*)
−53 skeleton tracing error
−54 region specified in clockwise order
−55 illegal ITNODE(3,*)
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Chapter 7
TRIGEN Parameters

IADAPT Definitions


IADAPT mesh generation option
0 error estimates only
1 refine or unrefine mesh using uh
-1 refine or unrefine mesh using QXY
2 unrefine and refine mesh using uh
-2 unrefine and refine mesh using QXY
3 smooth mesh points using uh
-3 smooth mesh points using QXY
4 uniform mesh refinement
-4 uniform degree refinement
5 skeleton → triangulation
6 load balance (MPI)
7 reconcile mesh (MPI)

IERRSW Definitions


IERRSW error recovery option
0 globally continuous recovery
1 patchwise continuous recovery

IRTYPE Definitions


IRTYPE adaptivity option
0 hp refinement / unrefinement
1 h refinement / unrefinement
-1 p refinement / unrefinement
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Chapter 8
PLTMG Parameters

IFIRST Definitions


IFIRST option
0 no initialization
1 initialize for piecewise linear elements
2 initialize for piecewise quadratic elements
3 initialize for piecewise cubic elements
4 initialize for piecewise quartic elements
5 initialize for piecewise quintic elements
6 initialize for piecewise polynomials of degree 6
7 initialize for piecewise polynomials of degree 7
8 initialize for piecewise polynomials of degree 8
9 initialize for piecewise polynomials of degree 9

IPROB Definitions


IPROB problem option
1 elliptic boundary value problem
2 obstacle problem
3 continuation problem
4 parameter identification problem
5 optimal control problem
-1DD solve for elliptic boundary value problem
-2DD solve for obstacle problem
-3DD solve for continuation problem
-4DD solve for parameter identification problem
-5DD solve for optimal control problem

ITASK Definitions


ITASK IPROB option
0 1 default
9 use functional
0 2 default
0 3continue to the nearest target point
1 continue to the nearest target or singular point
2 switch branches at a bifurcation point
3 switch λ and/or ρ; initialize with λ fixed
4 switch λ and/or ρ; initialize with ρ fixed
5 solve with σ = 0, θ = 0 (λ fixed)
6 solve with σ = 0, θ = 2 (ρ fixed)
7 solve with σ = 0, θ = 1
0 4default
8 λ affects domain shape
0 5 default

ISPD Definitions


ISPD storage/iteration options
0 nonsymmetric/biconjugate gradient
1 symmetric/conjugate gradient

METHOD Definitions


METHOD preconditioner
0 Block SGS smoother, HB coarse space
1 ILU
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Chapter 9
Graphics Parameters

IFUN Definitions


IFUN displayed function
0 the solution uh
1 the scalar function | ∇uh |
2 the vector function ∇uh
3 the alternate function QXY
4 the alternate vector function QXY
5 the error estimate || ϵt ||H1(t)
6 the tangent function · u
7 the right singular vector ψr
8 the left singular vector ψl
9 the Lagrange multiplier um
10the control variable λh
11the dual function ω
12the scaling factor αt

INPLSW Definitions


INPLSW triangulationskeleton
0 user label user label
1 load balance subregion
2 element quality
3 largest angle
4 smallest angle
5 mesh grading
6 polynomial degree
7 element diameter

IGRSW Definitions


IGRSW displayed graph
0 Newton iteration convergence history
1 CSCG/CSBCG iteration convergence history
-1 matrix statistics
2 individual subroutine timing statistics
-2 time pie chart
3 the continuation path
-3 load balance
4 error estimates for H1 norm
-4 error estimates for L2 norm
5 the IP array
-5the SP array
6 the RP array

Graphics Options


ISCALE scale
0 linear
1 logarithmic
2 sinh−1
LINES line drawing option
0 all triangle edges
1 boundary/interface edges
2 load balance boundary edges
3 contours
-1 underlying graphics triangulation
NUMBRS labeling option
0 no labels
1 triangles/subregions
2 vertices
3 edges
4 curved edges
5 edge type
6 edge labels
7 processor
8 vertex type
9 degrees of freedom
10 element degree
ICONT smoothing option
0 no smoothing
1 smooth piecewise constant function
MPIRGN image option
0 all processors contribute
I > 0 draw image from processor I
ICRSN coarsening option
0 no coarsening
1 coarsen global subspace
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On 25 Jun 2018, 13:53.