From cecefc905ffe4db4fc508ed57ef3c587483800c1 Mon Sep 17 00:00:00 2001 From: wolf Date: Mon, 20 Dec 1999 14:53:35 +0000 Subject: [PATCH] Add step-3. git-svn-id: https://svn.dealii.org/trunk@2088 0785d39b-7218-0410-832d-ea1e28bc413d --- .../chapter-2.step-by-step/navbar.html | 8 +++ .../step-3.data/solution-1.jpg | Bin 0 -> 15240 bytes .../step-3.data/solution-2.jpg | Bin 0 -> 13623 bytes .../chapter-2.step-by-step/step-3.intro | 14 +++++ .../chapter-2.step-by-step/step-3.results | 57 ++++++++++++++++++ .../tutorial/chapter-2.step-by-step/toc.html | 10 ++- 6 files changed, 87 insertions(+), 2 deletions(-) create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-2.jpg create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/navbar.html b/deal.II/doc/tutorial/chapter-2.step-by-step/navbar.html index e717a6de48..a25e1268cb 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/navbar.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/navbar.html @@ -24,16 +24,24 @@ Step-by-Step overview

+
  • Step 1

  • +
  • Step 2

  • + +
  • +

    + Step 3 +

    +
  • Back to the tutorial index diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg new file mode 100644 index 0000000000000000000000000000000000000000..1b44a311f4ec066f48f0097f39cfaeffd8e98c0a GIT binary patch literal 15240 zcmb_@Wl$W^w(cN70t5>>xCAFakl^k?g1c*AaLwQl90mr5Ai;tMA3V5AAOxGi1_|y? zfR}U5J?Gt9uil?mue++Ny1Htwy;m>!_Fmt5T6kIm5U409D*#YXPyqk90Z)$r5jtg% zrM)eky{(I_hozUT4V{%gowT#1jg6xVouY%Qre!_t@S z`4b!<3&6s_z{Gflg^7uYjg9pj_az=K4h}8_5i$NtYD!ufYDy|9Iwo!wItETgDk@eX zHclR1etv#h7Gd$Xd}7>h`1zi?0XSHIKPV0;D1?BgegM_qS)ro+V}Ad+(4V2AVW41Q z{rxIO06;}SM?phHdxnOM@$4A@fP#t!Kz~L^gh5Qt!26O<8k2%n-BG!MRTNU1LuGY}Y41v*gX!J^C%}Nx zT;!+!U%&SM#Y$>i%kR!h?_>n;S6PTm+?SSyZc-$}6q5V_`%<~wkA+>P+4r84rd1oI zcdqM)$Z7C+^2wJBrzUiE-fPna*Bv~!>p1;hGE7UQkpT^c8a2?cVB(eP!MjhYin{cNaYaI z|ImCbuYU2Pf1CGp9RTm(=1-+$Ta8FC3+|l0zTZyR30XiwV@FGFWm&$;%0{%C55JTI z`#JS&zJnhuPn5f`EePSrU$@2lX`u$zNc84SXd#w{J}lv;rjq39913&&eejY@a8Twu zMLc(0Ki-X@g!LV%_MQGro9iL4q^(RL^Ur5TueA>|zfVe;j=S}4J0W9rck{ac!v$;f ziRXyzIJsHEsmU{qdwf9@trugsTM@Q7k<*=cBT`mkPRSyb0T{Xs1`e*pFw!$oB?v)E zrk&glbOu6d#t8+C;9?ZCZ~QHG(|ZVbyZ)PZ!WaXKN?| zL(%d@=GyFysu|PU1`5(3ai;OdIKup<#;`-|GANPY$8gtH$)@u<%{6tQ zG|hCEF*SB}bc}ZuH%Cowk?0hfJmjW$6Oj7J)(<}HmlY+!tPpkhl5hh|a%GlyudzGX zu<@*ruCixBHE75_=VI7k*NYDXRpv$M8alJUvfEUDhJ9GzhH zmW$5A8h9DsjY!PG4P;4v<>?Jl_%22p!mo=7oirGU5X~z^g(w`g;14}&TM<7MiGgBm zCf3RA)h?WI0*IcG=K>T&smxx6avu)fhF9m_?8>Q$_fx3;k#J(>PmbJ7mZ_{Aw`rlH ze~zCfRRs*{4tZr{)Oom>*^YZzKlLGYP!&fYPxQALr|e{jo;(f3cs9E+;+DlN%xNs^ zF8jQQ^u#R@ySj$&m7xKT8TXefqyqC>5=qvL>fD&j8~b_~p_NBVj5behyD^!5(vonH zJDtY}=Lf+_@&u3%#v;lh+0ez-P9kE!e$LKyFxu#dGeW+VR2zY%6S~H#zuBSCkqr@u zRHRK)C4YSgIyygq>0KwkLbhilS@dUN0<~xtzVyFJ9qCHnv*3+gd6AZoSGFV|!mjXs$V&9J_NJc*L)HIIF6`lzJo6OoKqZUF z$t{Lfq6tU80jn1E7aazlK#o}^eiE9&lv}PMw7h}T(B(zsk$q(E+gF`J;|*$bap6&0 zE`N$xf>L(R48BNk)bGaI4$^)FadLmEO(*D%bNIywsG|c^#MNSkmr&44OBaa}@C{W^z0OZuo+qdy+oNoIrM_ z>M@M3?BRfwYc_jBsZLfjs4vtpxi_QQc`d#KDxu}_xHr^0 zy)qFf$sJTJ|0vfNGhQemVJuA?@P>q|*hOk^>ik$%v4;tzns7*hy~m@~ET?%wydx4g z0DX(kV~tx*lhs;gMijY*MKuY}A&e)zK{%7?#f7V0bx<9GR)L7DS2X1e(IG3DaJd0` znsmA(S&zx3`I6JZRjvTL99l2DriUW_t209-a(9Csq>aI%9|=w8UB}L|vz1AwdyaJH z@pDB8+qGBO$#UeUXv>%PcoVTTY5rK_$vY0GEa0h(&K&0Wy1cm~HXR#=C4%PjNU^U? 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    }5b}mo}J3AFZLZYU`DoG}d z$9T+`ScA|r)}&Pz!?GecQRKhUwIER}(f zXY7T7?xjah-vJaSEE^^bOo!%UcE2qI@gf=SMJ$kfqq!fk?psp42AC=M56k|;ym~&t z{Co~tfsgZ2!4{JAM(X#Na!Yf`!i5<1j)~Ti%$;7lJk<(ED;__6A8;Q^#Jj(5K8wLY z4EKc+N&~p(a6Xm-6hPoV(>7OLYWDo8R0?b-d<~Y#H%<|M5y{`)PBvUCqH(JDeMFY0))(W3Ro*(sz_``-HsdlC`vA#rF}VJ?#fw+tt3UV3XB3;; znp+eg1Rb9-vq4h*437$DQ#R*CE86oWUeK&=1d6%J!QNraZh%iiVX8~pOUG2Abw}D% zher~YZ$1?}8Kdt2=Wc&1_2Vah$Q`Gjp$D=I8^$ev&;3XV5Qm4eOGgH=svQd(9 zW<}s9oYTc}eP+cAp%t^%vOOFFfP_^DGRvbUXzE4=R`y<4JAn3`4atuM0i!|nn%oZq zf(H~Oeso+w!g!vCCqJGB-=?u5uuOgu}M6lcH}iTgIC zp_HQM^6g;j07sRfK5`udpOZYJ%l7)}B<}gSZ~|^&?KQoH^DyM=d+;6L>4#r1#)lKS zljWZ-*|EcNc`Y5c@`hvYXTSzq&h%;Epi&PP{eu zPaWN3B5Bb{-S$2dX8%35wMkD?USbv_<9v+fsU>dwLqCpn6~q=fF-7`}G2=hOvMj+g zC(?dyhkP2ZCxYuvOSMQ8ntFpjMC8D8LZuy8@twy1E5ZNYCMX^#K=IeYON5~_NM!mV zEmd7v9Fw55gJhJ)SkuX#XKpwV9KMP~MoU;m;i@q^)4h=I08jvcv3mbclK&$IhIe!S E3niZl>i_@% literal 0 HcmV?d00001 diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro new file mode 100644 index 0000000000..e8f16db009 --- /dev/null +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro @@ -0,0 +1,14 @@ + +

    Introduction

    + +This is the first example, where we actually use finite elements. We +will solve a simple version of Laplace's equation witht zero boundary +values, but a nonzero right hand side. This example is still quite +simple, but it already shows the basic structure of most finite +element programs, which are along the following lines: + diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results new file mode 100644 index 0000000000..6815f678d2 --- /dev/null +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results @@ -0,0 +1,57 @@ + +

    Results

    + +The output of the program looks as follows: +
    +
    +Number of active cells: 1024
    +Total number of cells: 1365
    +Number of degrees of freedom: 1089
    +DEAL:cg::Starting value 0.121094
    +DEAL:cg::Starting value 0.323075
    +DEAL:cg::Convergence step 47 value 5.33692e-13
    +
    +
    + +The first three lines is what we wrote to cout. The last +three lines were generated without our interaction by the CG +solver. The first two lines state the residual at the start of the +iteration, while the last line tells us that the solver needed 47 +iterations to bring the norm of the residual to 5.3e-13, i.e. below +the threshold 1e-12 which we have set in the `solve' function. We will +show in the next program how to suppress this output, which is +sometimes useful for debugging purposes, but often clutters up the +screen display. + +

    + +Apart from the output shown above, the program generated the file +solution.gpl, which is in GNUPLOT format. It can be +viewed as follows: invoke GNUPLOT and enter the following sequence of +commands at its prompt: +

    +
    +gnuplot> set data style lines
    +gnuplot> splot "solution.gpl"
    +
    +
    +This produces the picture of the solution below left. Alternatively, +you can order GNUPLOT to do some hidden line removal by the command +
    +
    +gnuplot> set hidden3d
    +
    +
    +to get the result at the right: +

    + + + + + +
    +solution-1 + +solution-2 +
    +

    diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html b/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html index df36f194b5..1e16ec2e09 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html @@ -40,17 +40,23 @@ At present, the following programs exist:

    Step 1
    -
    What's new: everything. We create a grid and show a simple +
    What's new: everything. We create a grid and show a simple way to write it to a file.
    Step 2
    -
    What's new: Associate degrees of freedom to each vertex +
    What's new: Associate degrees of freedom to each vertex and compute the resulting sparsity pattern of matrices. Show that renumbering reduces the bandwidth of matrices significantly, i.e. clusters nonzero entries around the diagonal.
    + +
    Step 3
    +
    What's new: Actually solve Laplace's + problem. Object-orientation. Assembling matrices and + vectors. Boundary values. +
    -- 2.39.5