Discussion of Tekton, GeoFEM & Adina

• Differences in development path• Differences in cost/support available• Differences in size and capabilities• Issues for solving large problems:

– Direct solution vs iterative solution– Serial vs parallel

• Shared vs distributed memory

• Disclaimer: informed opinion of non-expert

TEKTON 2.3 (aka Tecton)TEKTON is a finite element computer code that is tailored specifically to solve tectonic problems for geologists andgeophysicists. The FORTRAN source code is available at website http://www.lpl.arizona.edu/tekton/, along with advice from veteran users.

TEKTON has been developed over many years by [Jay Melosh and] numerous people (the first of whom was Arthur Raefsky). In addition to the old, very stable, program TECTON 1.51, you will also find TEKTON 2.3. This is a much more advanced version that employs sparse matrix storage methods and hence can solve 3-D problems quite efficiently. If you use this version, please regard it as a beta-test version. I intend to upgrade TEKTON 2.3 very shortly . . . .

Last Updated: June 4, 1999

TEKTON 2.3

• Linear shape functions, brick elements

• Direct solution of Kd = f• High accuracy• sparse matrix

• Memory ~ n5/3 (n = number of nodes)• Time to factor K ~ n5/3 ; to solve ~ n2

• N ~ nedge3; M ~ nedge

5; t ~ nedge6

TEKTON 2.1 – Charles Williams

• Iterative solution of Kd = f• Accuracy?• Rate of convergence?

• Memory ~ n (n = number of nodes)

• Time to solve ~ n4/3 ~ nedge4

• Could have parallel implementation– Distributed memory

GeoFEM“Solid” Earth component of

Earth Simulator Project

http://geofem.tokyo.rist.or.jp/

 

                                                                                                                                                  

                                                                                            

3D Linear-Elastic Problem with 800M DOF on 128 nodes of the Hitachi SR8000 at the University of Tokyo by 335 GFLOPS performance.(December 10, 2001)

                          

4th GeoFEM Seminar                                    The University of Tokyo, Japan July 18, 2002 >> DETAIL (Japanese)

>> DETAIL (PDF FILE 157KB)

                          

SSS2001 Workshop on Scalable Solver Software  December 3-5, 2001  The University of Tokyo >> DETAIL

 

    

                                                                     

                                                                     

                                                                     

                                                                     

                                                                     

                                                                     

                                                                     

                                                                               

Research Organization for Information Science & Technology (RIST)  2-2-54, Nakameguro, Meguro-ku Tokyo, 153-0061, Japan 

TEL: +81-3-3712-5321 FAX: +81-3-3712-5552  http://www.tokyo.rist.or.jp/

Copyright(C)2001 Research Organization for Information Science & Technology (RIST) All Rights Reserved.

                                                                                                                                                                                    

                                                                                                                                                                

Top >> Software Download

 

GeoFEM Software Download

    GeoFEM Version 4.0 Download •GeoFEM Version 4.0 Basic Distribution Kit•Collection of GeoFEM Version 4.0 Sample Data•Thermal Fluid Analysis Subsystem for GeoFEM Version 4.0

    Patch files for GeoFEM Version 4.0 Download     GPPView beta version (GeoFEM Pre/Post Viewer Editor)    GeoFEM Manual Download

•English•GeoFEM/Tiger Quick Start Ver.4.0 E  "English Version"

•Japanese•GeoFEM/Tiger Quick Start Ver.4.0 J "Japanese Version"•"Static_Linear" Module User's Manual•"Dynamic_Linear" Module User's Manual•"Thermal" Module User's Manual•"Plug-in" Manual

   Availability of GeoFEM Software (Platform and Parameters)    GeoFEM FAQ    GeoFEM Online Tutorial

                                                                                                                                                                

GeoFEM node partitioning

Grid partitioning – Recursive Coordinate Bisection, METIS

Example partitioning

Speed, memory comparison TEKTON 2.3,

2.1 vs GeoFEM• GeoFEM – elastic only (released now)• Elastic - numerically challenging step

– Stress singularity at fault tip

• Correspondence principal – viscoelastic

• Do iterative techniques converge quickly?

Try Benchmark 4?Finite length strike-slip dislocation in rigid-walled box

Kluge: Use ½ box, impose dislocation as boundary condition

GeoFEM Definition Language . . . . begin structure_static_linear!  format_version  4.0  title           example_used_for_caltech  analysis        elastic!      begin solver      method                      CG      precondition                SSOR!   .. solver parameters ..!         integer ; max. iteration, restart for GMRES!         real    ; conv. tol, diag. mul, non-diag. mul.      integer_parameter           20000      integer_parameter               1      real_parameter              1.0e-7      real_parameter              1.0      real_parameter              0.0    end!

Run time vs n

• Tekton 2.3 direct solve: t ~ n2

• Tecton 2.1, GeoFEM iterative solve t ~ n4/3

Tecton 2.1 vs GeoFEM times

• Run times comparable• Different preconditioners (IC(?) vs

SSOR)• Convergence criteria the same??

memory vs n

• Tekton 2.3 direct solve: M ~ n1.5

– Expected M ~ n1.67; non-K memory affects small n

• Tecton 2.1, GeoFEM iterative solve M ~ n

GeoFEM parallel performance

• Efficiency (e = t1/(N tN) and runtime

• tN vs number of processors, N

• 4 processor PC cluster

GeoFEM parallel performance

• Iteration inefficiency and memory/processor vs number of processors

• Splitting the problem requires more iterations

Summary of elastic tests

• Iterative solution works!• Performance depends on

preconditioner• Scalings with n as expected• Scalings with N look good• Need to extend comparisons to

variable grid and variable modulus

Adina

• http://www.adina.com/• MIT heritage (Bathe)• Commercial code• Many element types• Many rheological descriptions,

dynamic, . . .• Shared memory• NOT distributed memory• Plan to use for benchmarks

Benchmark 7 Elastic solution for a circular strike-slip fault. The purpose of this problem is to address how well our codes handle curved faults. By symmetry, the radial displacements should vanish. The conceptual model is an elastic disk of radius 200 km, with a circular left-lateral strike-slip fault forming an inner plug rotating inside an outer annulus. Because of the symmetry of the problem, only the first quadrant needs to be calculated.

Analytic solution for infinite halfspace from Okada for comparison

Okada solution

Benchmark 7 GridGrid for benchmark 7: 40 km thick quarter disk; free at top, pinned at bottom

u_x pinned, u_y, u_z free

u_y pinned, u_x, u_z free

Benchmark 7 – GAEA, r=100 kmGAEA BM7 (quadratic serendipity brick elements)r = 100 km; average displacement (no split)x dot u x cross udot/crossX Y u_x u_y u_z flt_perp flt_parallel(m) (m) (m) (m) (m) (cm) (cm)100000 0 0 -0.1332 0 0.0000 -13.32 0.00%99690 7846 0.0119 -0.142 -0.002 0.0722 -14.25 -0.51%98770 15640 0.0229 -0.1458 0.001 -0.0185 -14.76 0.13%97240 23340 0.0339 -0.1419 1E-04 -0.0155 -14.59 0.11%95110 30900 0.0448 -0.1381 2E-04 -0.0064 -14.52 0.04%92390 38270 0.0558 -0.1346 -1E-04 0.0042 -14.57 -0.03%89100 45400 0.0662 -0.13 2E-04 -0.0036 -14.59 0.02%85260 52250 0.0762 -0.1243 0 0.0021 -14.58 -0.01%80900 58780 0.0857 -0.1179 0 0.0030 -14.58 -0.02%76040 64940 0.0946 -0.1108 0 -0.0020 -14.57 0.01%70710 70710 0.1031 -0.1031 0 0.0000 -14.58 0.00%64950 76040 0.1109 -0.0947 0 0.0020 -14.58 -0.01%58780 80900 0.1179 -0.0857 0 -0.0030 -14.58 0.02%52250 85260 0.1242 -0.0761 0 0.0012 -14.57 -0.01%45400 89100 0.13 -0.0662 -2E-04 0.0036 -14.59 -0.02%38270 92390 0.1346 -0.0558 1E-04 -0.0042 -14.57 0.03%30900 95110 0.1381 -0.0448 -2E-04 0.0064 -14.52 -0.04%23350 97240 0.1419 -0.034 -1E-04 0.0072 -14.59 -0.05%15640 98770 0.1458 -0.0229 -0.001 0.0185 -14.76 -0.13%7847 99690 0.142 -0.0119 0.002 -0.0720 -14.25 0.51%

0 100000 0.1332 0 0 0.0000 -13.32 0.00%Okada (1/2 space):-17.92

Benchmark 7 – GAEA, r=120 kmGAEA BM7 (quadratic serendipity brick elements)r = 120 km; average displacement (no split) x dot u x cross udot/crossX Y u_x u_y u_z flt_perp flt_parallel(m) (m) (m) (m) (m) (cm) (cm)120000 0 0 0.0989 0 0.0000 11.87 0.00%119600 9415 -0.0102 0.0992 0.0003 -0.2860 11.96 -2.39%118500 18770 -0.0144 0.0978 -0.0003 0.1293 11.86 1.09%116700 28010 -0.0227 0.0957 -0.0001 0.0315 11.80 0.27%114100 37080 -0.0306 0.0944 0 0.0089 11.91 0.07%110900 45920 -0.0378 0.0913 0 0.0005 11.86 0.00%106900 54480 -0.0449 0.0883 0 0.0108 11.89 0.09%102300 62700 -0.0517 0.0844 0 0.0030 11.88 0.03%97080 70530 -0.0582 0.0801 0 -0.0006 11.88 -0.01%91250 77930 -0.0642 0.0752 0 0.0021 11.87 0.02%84850 84850 -0.07 0.07 0 0.0000 11.88 0.00%77930 91250 -0.0752 0.0642 0 -0.0021 11.87 -0.02%70530 97080 -0.0801 0.0582 0 0.0006 11.88 0.01%62700 102300 -0.0844 0.0517 0 -0.0030 11.88 -0.03%54480 106900 -0.0883 0.0449 0 -0.0108 11.89 -0.09%45920 110900 -0.0913 0.0378 0 -0.0005 11.86 0.00%37080 114100 -0.0944 0.0306 0 -0.0089 11.91 -0.07%28010 116700 -0.0957 0.0227 0.0001 -0.0315 11.80 -0.27%18770 118500 -0.0978 0.0144 0.0003 -0.1293 11.86 -1.09%9416 119600 -0.0992 0.0102 -0.0003 0.2859 11.96 2.39%

0 120000 -0.0989 0 0 0.0000 11.87 0.00%Okada 1/2 space: 10.12

Benchmark 7 – ABAQUS, r=120 km, linear elementsABAQUS, linear elements, 10 km spacing

x y u_x u_y u_z r x * u x X u */X(km) (km) (km) (km) (km) (km) flt perp flt paralperp/paral

(cm) (cm)120.00 0.00 -4.67E-23 -2.11E-07 -1.01E-07 120 0.0000 -25.26 0.00%119.63 9.42 -3.11E-09 -1.96E-07 -4.83E-08 120 -2.2195 -23.45 9.47%118.52 18.77 2.37E-08 -1.77E-07 -1.79E-08 120 -0.5123 -21.43 2.39%116.68 28.01 3.33E-08 -1.62E-07 -4.84E-09 120 -0.6390 -19.80 3.23%114.13 37.08 4.81E-08 -1.49E-07 -9.05E-10 120 -0.0343 -18.77 0.18%110.87 45.92 5.56E-08 -1.40E-07 3.39E-10 120 -0.2837 -18.12 1.57%106.92 54.48 6.80E-08 -1.33E-07 2.25E-10 120 0.0037 -17.97 -0.02%102.32 62.70 7.61E-08 -1.26E-07 2.37E-10 120 -0.1295 -17.69 0.73%97.08 70.53 8.70E-08 -1.20E-07 7.73E-12 120 0.0041 -17.75 -0.02%91.25 77.93 9.49E-08 -1.12E-07 3.17E-11 120 -0.0382 -17.58 0.22%84.85 84.85 1.04E-07 -1.04E-07 -1.21E-22 120 0.0000 -17.71 0.00%77.93 91.25 1.12E-07 -9.49E-08 -3.17E-11 120 0.0382 -17.58 -0.22%70.53 97.08 1.20E-07 -8.70E-08 -7.73E-12 120 -0.0041 -17.75 0.02%62.70 102.32 1.26E-07 -7.61E-08 -2.37E-10 120 0.1295 -17.69 -0.73%54.48 106.92 1.33E-07 -6.80E-08 -2.25E-10 120 -0.0037 -17.97 0.02%45.92 110.87 1.40E-07 -5.56E-08 -3.39E-10 120 0.2837 -18.12 -1.57%28.01 116.68 1.62E-07 -3.33E-08 4.84E-09 120 0.6390 -19.80 -3.23%18.77 118.52 1.77E-07 -2.37E-08 1.79E-08 120 0.5123 -21.43 -2.39%9.42 119.63 1.96E-07 3.11E-09 4.83E-08 120 2.2195 -23.45 -9.47%0.00 120.00 2.11E-07 -2.36E-23 1.01E-07 120 0.0000 -25.26 0.00%

Benchmark 7 – ABAQUS, r=120 km, quadratic elementsABAQUS, quadratic elements, 10 km spacing, r=120 km

x y u_x u_y u_z r x * u x X u */X(km) (km) (km) (km) (km) (km) flt perp flt paralperp/paral

(cm) (cm)120.00 0.00 -4.58E-23 -2.06E-07 -9.62E-08 120 0.0000 -24.76 0.00%119.26 9.39 1.86E-09 -2.04E-07 -4.78E-08 120 -1.6957 -24.37 6.96%118.52 18.77 2.44E-08 -1.81E-07 -1.91E-08 120 -0.4950 -21.86 2.26%116.32 27.93 3.65E-08 -1.68E-07 -6.24E-09 120 -0.4646 -20.62 2.25%114.13 37.08 4.83E-08 -1.56E-07 -1.89E-09 120 -0.2498 -19.54 1.28%110.52 45.78 6.03E-08 -1.50E-07 -1.99E-10 120 -0.1794 -19.29 0.93%106.92 54.48 6.97E-08 -1.39E-07 1.63E-11 120 -0.1018 -18.62 0.55%102.00 62.51 8.18E-08 -1.35E-07 6.31E-11 120 -0.0708 -18.84 0.38%97.08 70.53 8.97E-08 -1.24E-07 5.61E-11 120 -0.0415 -18.37 0.23%90.97 77.69 1.02E-07 -1.19E-07 -3.75E-12 120 -0.0211 -18.72 0.11%84.85 84.85 1.08E-07 -1.08E-07 -1.07E-23 120 0.0000 -18.32 0.00%77.69 90.97 1.19E-07 -1.02E-07 3.75E-12 120 0.0211 -18.72 -0.11%70.53 97.08 1.24E-07 -8.97E-08 -5.61E-11 120 0.0415 -18.37 -0.23%62.51 102.00 1.35E-07 -8.18E-08 -6.31E-11 120 0.0708 -18.84 -0.38%54.48 106.92 1.39E-07 -6.97E-08 -1.63E-11 120 0.1018 -18.62 -0.55%45.78 110.52 1.50E-07 -6.03E-08 1.99E-10 120 0.1794 -19.29 -0.93%37.08 114.13 1.56E-07 -4.83E-08 1.89E-09 120 0.2498 -19.54 -1.28%27.93 116.32 1.68E-07 -3.65E-08 6.24E-09 120 0.4646 -20.62 -2.25%9.39 119.26 2.04E-07 -1.86E-09 4.78E-08 120 1.6957 -24.37 -6.96%0.00 120.00 2.06E-07 -2.31E-23 9.62E-08 120 0.0000 -24.76 0.00%

Benchmark 7 – ABAQUS, r=120 km, quadratic elementsABAQUS quadratic elements, 5 km spacing, r = 120 km,

x y u_x u_y u_z r x * u x X u */X(km) (km) (km) (km) (km) (km) flt perp flt paral

(cm) (cm)120.00 0.00 -4.74E-23 -2.13E-07 -9.20E-08 120 0.0000 -25.61 0.00%119.82 4.71 -5.43E-09 -2.11E-07 -6.79E-08 120 -1.6453 -25.30 6.50%119.63 9.42 5.75E-09 -2.04E-07 -4.66E-08 120 -1.2290 -24.41 5.03%119.08 14.09 1.31E-08 -1.96E-07 -3.05E-08 120 -1.2005 -23.49 5.11%118.52 18.77 2.23E-08 -1.86E-07 -1.91E-08 120 -0.8456 -22.42 3.77%117.60 23.39 2.96E-08 -1.78E-07 -1.15E-08 120 -0.6852 -21.61 3.17%116.68 28.01 3.66E-08 -1.70E-07 -6.60E-09 120 -0.4832 -20.81 2.32%115.41 32.55 4.29E-08 -1.64E-07 -3.53E-09 120 -0.3860 -20.32 1.90%114.13 37.08 4.88E-08 -1.58E-07 -1.77E-09 120 -0.2878 -19.82 1.45%112.50 41.50 5.47E-08 -1.54E-07 -7.36E-10 120 -0.2308 -19.56 1.18%110.87 45.92 6.00E-08 -1.49E-07 -2.28E-10 120 -0.1781 -19.25 0.93%108.89 50.20 6.58E-08 -1.46E-07 3.62E-11 120 -0.1439 -19.15 0.75%106.92 54.48 7.09E-08 -1.41E-07 1.17E-10 120 -0.1136 -18.95 0.60%104.62 58.59 7.65E-08 -1.38E-07 1.39E-10 120 -0.0914 -18.92 0.48%102.32 62.70 8.13E-08 -1.34E-07 1.11E-10 120 -0.0720 -18.79 0.38%99.70 66.62 8.68E-08 -1.31E-07 8.33E-11 120 -0.0564 -18.81 0.30%97.08 70.53 9.14E-08 -1.26E-07 5.07E-11 120 -0.0427 -18.71 0.23%94.17 74.23 9.66E-08 -1.23E-07 3.02E-11 120 -0.0308 -18.75 0.16%91.25 77.93 1.01E-07 -1.18E-07 1.40E-11 120 -0.0200 -18.67 0.11%88.05 81.39 1.06E-07 -1.15E-07 5.83E-12 120 -0.0098 -18.73 0.05%84.85 84.85 1.10E-07 -1.10E-07 -6.00E-22 120 0.0000 -18.66 0.00%