func Test_nurbs01(tst *testing.T) {
/* 4 (1,2) (2,2) 6
5 2@o--------------o@3 7
| |
| | @ -- control point
| | o -- node
| | (a,b) -- span
| |
| |
0 0@o--------------o@1 2
1 (1,1) (2,1) 3
*/
//verbose()
chk.PrintTitle("nurb01. square with initial stress")
// fem
analysis := NewFEM("data/nurbs01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectors
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// draw NURBS
if false {
nurbs := dom.Msh.Cells[0].Shp.Nurbs
gm.PlotNurbs("/tmp/gofem", "test_nurbs01", nurbs, 21, false, nil)
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 4)
chk.IntAssert(len(dom.Elems), 1)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 2)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "eqs", eqs, utl.IntRange(4*2))
chk.Ints(tst, "nids", nids, []int{0, 1, 2, 3})
// check Umap
Umaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7},
}
for i, ele := range dom.Elems {
e := ele.(*ElemU)
io.Pfpink("%2d : Umap = %v\n", e.Id(), e.Umap)
chk.Ints(tst, "Umap", e.Umap, Umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 4)
var ct_ux_eqs []int // equations with ux prescribed [sorted]
var ct_uy_eqs []int // equations with uy prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pfgrey("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "ux":
ct_ux_eqs = append(ct_ux_eqs, eq)
case "uy":
ct_uy_eqs = append(ct_uy_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_ux_eqs)
sort.Ints(ct_uy_eqs)
chk.Ints(tst, "equations with ux prescribed", ct_ux_eqs, []int{0, 4})
chk.Ints(tst, "equations with uy prescribed", ct_uy_eqs, []int{1, 3})
// check displacements
tolu := 1e-16
for _, n := range dom.Nodes {
eqx := n.GetEq("ux")
eqy := n.GetEq("uy")
u := []float64{dom.Sol.Y[eqx], dom.Sol.Y[eqy]}
chk.Vector(tst, "u", tolu, u, nil)
}
// analytical solution
qnV, qnH := -100.0, -50.0
ν := 0.25
σx, σy := qnH, qnV
σz := ν * (σx + σy)
σref := []float64{σx, σy, σz, 0}
// check stresses
e := dom.Elems[0].(*ElemU)
tols := 1e-13
for idx, _ := range e.IpsElem {
σ := e.States[idx].Sig
io.Pforan("σ = %v\n", σ)
chk.Vector(tst, "σ", tols, σ, σref)
}
}
func Test_up01a(tst *testing.T) {
/* this tests simulates seepage flow along a column
* by reducing the initial hydrostatic pressure at
* at the bottom of the column
*
* using mesh from col104elay.msh
*
* Nodes / Tags Equations
* ux uy pl ux uy pl
* 8 o----o----o 9 (-5) 53 54 55 o----o----o 50 51 52
* | 14 | . . . | 58 59 | . . .
* | (-1) | . . . | | . . .
* 21 o o o 22 (-6) 60 61 . o o o 56 57 .
* | 26 | . . . | 62 63 | . . .
* | | . . . | | . . .
* 6 o----o----o 7 (-4) 39 40 41 o----o----o 36 37 38
* | 13 | . . . | 44 45 | . . .
* | (-1) | . . . | | . . .
* 19 | o o 20 (-6) 46 47 . | o o 42 43 .
* | 25 | . . . | 48 49 | . . .
* | | . . . | | . . .
* 4 o----o----o 5 (-3) 25 26 27 o----o----o 22 23 24
* | 12 | . . . | 30 31 | . . .
* | (-2) | . . . | | . . .
* 17 o o o 18 (-6) 32 33 . o o o 28 29 .
* | 24 | . . . | 34 35 | . . .
* | | . . . | | . . .
* 2 o----o----o 3 (-2) 9 10 11 o----o----o 6 7 8
* | 11 | . . . | 16 17 | . . .
* | (-2) | . . . | | . . .
* 15 o o o 16 (-6) 18 19 o o o 14 15
* | 23 | . . . | 20 21 | . . .
* | | . . . | | . . .
* 0 o----o----o 1 (-1) 0 1 2 o----o----o 3 4 5
* 10 12 13
*/
// capture errors and flush log
defer End()
//verbose()
chk.PrintTitle("up01a")
// start simulation
if !Start("data/up01.sim", true, chk.Verbose) {
chk.Panic("cannot start simulation")
}
// domain
distr := false
dom := NewDomain(Global.Sim.Regions[0], distr)
if dom == nil {
chk.Panic("cannot allocate new domain")
}
// set stage
if !dom.SetStage(0, Global.Sim.Stages[0], distr) {
chk.Panic("cannot set stage")
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 27)
chk.IntAssert(len(dom.Elems), 4)
if true {
// nodes with pl
nods_with_pl := map[int]bool{0: true, 2: true, 4: true, 6: true, 8: true, 1: true, 3: true, 5: true, 7: true, 9: true}
// check dofs
for _, nod := range dom.Nodes {
if nods_with_pl[nod.Vert.Id] {
chk.IntAssert(len(nod.Dofs), 3)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
chk.StrAssert(nod.Dofs[2].Key, "pl")
} else {
chk.IntAssert(len(nod.Dofs), 2)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
}
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "eqs", eqs, utl.IntRange(10*3+17*2))
chk.Ints(tst, "nids", nids, []int{
0, 1, 3, 2, 10, 16, 11, 15, 23,
5, 4, 18, 12, 17, 24,
7, 6, 20, 13, 19, 25,
9, 8, 22, 14, 21, 26,
})
// check pmap
Pmaps := [][]int{
{2, 5, 8, 11},
{11, 8, 24, 27},
{27, 24, 38, 41},
{41, 38, 52, 55},
}
Umaps := [][]int{
{0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21},
{9, 10, 6, 7, 22, 23, 25, 26, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35},
{25, 26, 22, 23, 36, 37, 39, 40, 30, 31, 42, 43, 44, 45, 46, 47, 48, 49},
{39, 40, 36, 37, 50, 51, 53, 54, 44, 45, 56, 57, 58, 59, 60, 61, 62, 63},
}
for i, ele := range dom.Elems {
e := ele.(*ElemUP)
io.Pfpink("%2d : Pmap = %v\n", e.Id(), e.P.Pmap)
io.Pfpink("%2d : Umap = %v\n", e.Id(), e.U.Umap)
chk.Ints(tst, "Pmap", e.P.Pmap, Pmaps[i])
chk.Ints(tst, "Umap", e.U.Umap, Umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 9*2+2+3)
var ct_ux_eqs []int // equations with ux prescribed [sorted]
var ct_uy_eqs []int // equations with uy prescribed [sorted]
var ct_pl_eqs []int // equations with pl prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pfgrey("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "ux":
ct_ux_eqs = append(ct_ux_eqs, eq)
case "uy":
ct_uy_eqs = append(ct_uy_eqs, eq)
case "pl":
ct_pl_eqs = append(ct_pl_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_ux_eqs)
sort.Ints(ct_uy_eqs)
sort.Ints(ct_pl_eqs)
chk.Ints(tst, "equations with ux prescribed", ct_ux_eqs, []int{0, 3, 6, 9, 14, 18, 22, 25, 28, 32, 36, 39, 42, 46, 50, 53, 56, 60})
chk.Ints(tst, "equations with uy prescribed", ct_uy_eqs, []int{1, 4, 13})
chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{2, 5})
}
// initial values @ nodes
io.Pforan("initial values @ nodes\n")
for _, nod := range dom.Nodes {
z := nod.Vert.C[1]
for _, dof := range nod.Dofs {
u := dom.Sol.Y[dof.Eq]
switch dof.Key {
case "ux":
chk.Scalar(tst, io.Sf("nod %3d : ux(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
case "uy":
chk.Scalar(tst, io.Sf("nod %3d : uy(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
case "pl":
plC, _, _ := Global.HydroSt.Calc(z)
chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-13, u, plC)
}
}
}
// intial values @ integration points
io.Pforan("initial values @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemUP)
for idx, ip := range e.P.IpsElem {
s := e.P.States[idx]
z := e.P.Shp.IpRealCoords(e.P.X, ip)[1]
chk.AnaNum(tst, io.Sf("sl(z=%11.8f)", z), 1e-17, s.A_sl, 1, chk.Verbose)
}
}
// parameters
ν := 0.2 // Poisson's coefficient
K0 := ν / (1.0 - ν) // earth pressure at rest
nf := 0.3 // porosity
sl := 1.0 // saturation
ρL := 1.0 // intrinsic (real) density of liquid
ρS_top := 2.0 // intrinsic (real) density of solids in top layer
ρS_bot := 3.0 // intrinsic (real) density of solids in bottom layer
h := 5.0 // height of each layer
g := 10.0 // gravity
// densities
nl := nf * sl // volume fraction of luqid
ns := 1.0 - nf // volume fraction of solid
ρl := nl * ρL // partial density of liquid
ρs_top := ns * ρS_top // partial density of solids in top layer
ρs_bot := ns * ρS_bot // partial density of solids in bottom layer
ρ_top := ρl + ρs_top // density of mixture in top layer
ρ_bot := ρl + ρs_bot // density of mixture in bottom layer
// absolute values of stresses
σV_z5 := ρ_top * g * h // total vertical stress @ elevation z = 5 m (absolute value)
σV_z0 := σV_z5 + ρ_bot*g*h // total vertical stress @ elevation z = 0 m (absolute value)
io.Pfyel("ρ_top = %g\n", ρ_top)
io.Pfyel("ρ_bot = %g\n", ρ_bot)
io.Pfyel("|ΔσV_top| = %g\n", ρ_top*g*h)
io.Pfyel("|ΔσV_bot| = %g\n", ρ_bot*g*h)
io.PfYel("|σV|(@ z=0) = %g\n", σV_z0)
io.PfYel("|σV|(@ z=5) = %g\n", σV_z5)
// stress functions
var sig fun.Pts
var pres fun.Pts
sig.Init(fun.Prms{
&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: -σV_z0},
&fun.Prm{N: "t1", V: 5.00}, {N: "y1", V: -σV_z5},
&fun.Prm{N: "t2", V: 10.00}, {N: "y2", V: 0.0},
})
pres.Init(fun.Prms{
&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: 100},
&fun.Prm{N: "t1", V: 10.00}, {N: "y1", V: 0},
})
// check stresses
io.Pforan("initial stresses @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemUP)
for idx, ip := range e.U.IpsElem {
z := e.U.Shp.IpRealCoords(e.U.X, ip)[1]
σe := e.U.States[idx].Sig
sv := sig.F(z, nil)
sve := sv + pres.F(z, nil)
she := sve * K0
if math.Abs(σe[2]-σe[0]) > 1e-17 {
tst.Errorf("[1;31mσx is not equal to σz: %g != %g[0m\n", σe[2], σe[0])
return
}
if math.Abs(σe[3]) > 1e-17 {
tst.Errorf("[1;31mσxy is not equal to zero: %g != 0[0m\n", σe[3])
return
}
chk.AnaNum(tst, io.Sf("sx(z=%11.8f)", z), 0.0003792, σe[0], she, chk.Verbose)
chk.AnaNum(tst, io.Sf("sy(z=%11.8f)", z), 0.001517, σe[1], sve, chk.Verbose)
}
}
return
}
func Test_sg52a(tst *testing.T) {
/* Smith & Griffths (5th ed) Figure 5.2 p173
*
* 0.25 0.5 0.25 kN/m
* ↓ ↓ ↓
* --- ▷0---------1---------2
* | | ,'| ,'| E = 1e6 kN/m²
* | | 0 ,' | 2 ,' | ν = 0.3
* | | ,' | ,' |
* | ,' 1 | ,' 3 | connectivity:
* 1 m ▷3'--------4'--------5 0 : 1 0 3
* | ,'| ,'| 1 : 3 4 1
* | | 4 ,' | 6 ,' | 2 : 2 1 4
* | | ,' | ,' | 3 : 4 5 2
* | | ,' 5 | ,' 7 | 4 : 4 3 6
* --- ▷6'--------7'--------8 5 : 6 7 4
* △ △ △ 6 : 5 4 7
* 7 : 7 8 5
* |------- 1 m -------|
*/
//verbose()
chk.PrintTitle("sg52a")
// start simulation
analysis := NewFEM("data/sg52.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 9)
chk.IntAssert(len(dom.Elems), 8)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 2)
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{1, 0, 3, 4, 2, 5, 6, 7, 8})
chk.Ints(tst, "eqs", eqs, []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17})
// check solution arrays
ny := 9 * 2
nλ := 6
nyb := ny + nλ
chk.IntAssert(len(dom.Sol.Y), ny)
chk.IntAssert(len(dom.Sol.Dydt), 0)
chk.IntAssert(len(dom.Sol.D2ydt2), 0)
chk.IntAssert(len(dom.Sol.Psi), 0)
chk.IntAssert(len(dom.Sol.Zet), 0)
chk.IntAssert(len(dom.Sol.Chi), 0)
chk.IntAssert(len(dom.Sol.L), nλ)
chk.IntAssert(len(dom.Sol.ΔY), ny)
// check linear solver arrays
chk.IntAssert(len(dom.Fb), nyb)
chk.IntAssert(len(dom.Wb), nyb)
// check umap
umaps := [][]int{
{0, 1, 2, 3, 4, 5},
{4, 5, 6, 7, 0, 1},
{8, 9, 0, 1, 6, 7},
{6, 7, 10, 11, 8, 9},
{6, 7, 4, 5, 12, 13},
{12, 13, 14, 15, 6, 7},
{10, 11, 6, 7, 14, 15},
{14, 15, 16, 17, 10, 11},
}
for i, ele := range dom.Elems {
e := ele.(*ElemU)
io.Pforan("e%d.umap = %v\n", e.Id(), e.Umap)
chk.Ints(tst, "umap", e.Umap, umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), nλ)
var ct_ux_eqs []int // constrained ux equations [sorted]
var ct_uy_eqs []int // constrained uy equations [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pforan("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "ux":
ct_ux_eqs = append(ct_ux_eqs, eq)
case "uy":
ct_uy_eqs = append(ct_uy_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_ux_eqs)
sort.Ints(ct_uy_eqs)
chk.Ints(tst, "constrained ux equations", ct_ux_eqs, []int{2, 4, 12})
chk.Ints(tst, "constrained uy equations", ct_uy_eqs, []int{13, 15, 17})
// point loads
chk.IntAssert(len(dom.PtNatBcs.Bcs), 3)
chk.StrAssert(dom.PtNatBcs.Bcs[0].Key, "fuy")
chk.StrAssert(dom.PtNatBcs.Bcs[1].Key, "fuy")
chk.StrAssert(dom.PtNatBcs.Bcs[2].Key, "fuy")
chk.IntAssert(dom.PtNatBcs.Bcs[0].Eq, 3)
chk.IntAssert(dom.PtNatBcs.Bcs[1].Eq, 1)
chk.IntAssert(dom.PtNatBcs.Bcs[2].Eq, 9)
}
func Test_phi01(tst *testing.T) {
/* Nodes Equations:
* 7 15
* 6 o----o----o----o----o 8 16 o----o----o----o----o 21
* | 13 | 14 | | 18 | 23 |
* | | | | | |
* 18 o [2] o19 [3] o 20 19 o o o17 o o 22
* | 23 | 24 | | 20 | 24 |
* | | | | | |
* 3 o----o----o----o----o 5 3 o----o----o----o----o 10
* | 11 4| 12 | | 6 2| 13 |
* | | | | | |
* 15 o [0] o16 [1] o 17 7 o o o5 o o 12
* | 21 | 22 | | 8 | 14 |
* | | | | | |
* 0 o----o----o----o----o 2 0 o----o----o----o----o 9
* 9 1 10 4 1 11
*/
//verbose()
chk.PrintTitle("phi01a")
// make sure to flush log
defer End()
// start simulation
if !Start("data/phi01.sim", true, chk.Verbose) {
tst.Errorf("test failed\n")
return
}
// domain
distr := false
dom := NewDomain(Global.Sim.Regions[0], distr)
if dom == nil {
tst.Errorf("test failed\n")
return
}
// set stage
if !dom.SetStage(0, Global.Sim.Stages[0], distr) {
tst.Errorf("test failed\n")
return
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 25)
chk.IntAssert(len(dom.Elems), 4)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 1)
chk.StrAssert(nod.Dofs[0].Key, "h")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{
0, 1, 4, 3, 9, 16, 11, 15, 21, 2, 5, 10, 17, 12, 22, 7, 6, 19, 13, 18, 23, 8, 20, 14, 24,
})
chk.Ints(tst, "eqs", eqs, []int{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
})
/*
// check pmap
pmaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8},
{3, 2, 9, 10, 6, 11, 12, 13, 14},
{10, 9, 15, 16, 12, 17, 18, 19, 20},
{16, 15, 21, 22, 18, 23, 24, 25, 26},
}
for i, ele := range dom.Elems {
e := ele.(*ElemP)
io.Pforan("e%d.pmap = %v\n", e.Id(), e.Pmap)
chk.Ints(tst, "pmap", e.Pmap, pmaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 3)
var ct_pl_eqs []int // equations with pl prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pforan("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "pl":
ct_pl_eqs = append(ct_pl_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_pl_eqs)
chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{0, 1, 4})
// initial values @ nodes
io.Pforan("initial values @ nodes\n")
for _, nod := range dom.Nodes {
z := nod.Vert.C[1]
eq := nod.Dofs[0].Eq
pl := dom.Sol.Y[eq]
plC, _, _ := Global.HydroSt.Calc(z)
chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, pl), 1e-17, pl, plC)
}
// intial values @ integration points
io.Pforan("initial values @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemP)
for idx, ip := range e.IpsElem {
s := e.States[idx]
z := e.Shp.IpRealCoords(e.X, ip)[1]
_, ρLC, _ := Global.HydroSt.Calc(z)
chk.Scalar(tst, io.Sf("sl(@ %18g)= %18g", z, s.A_sl), 1e-17, s.A_sl, 1)
chk.Scalar(tst, io.Sf("ρL(@ %18g)= %18g", z, s.A_ρL), 1e-13, s.A_ρL, ρLC)
}
}
*/
}
func Test_phi01(tst *testing.T) {
/* Nodes Equations:
* 7 15
* 6 o----o----o----o----o 8 16 o----o----o----o----o 21
* | 13 | 14 | | 18 | 23 |
* | | | | | |
* 18 o [2] o19 [3] o 20 19 o o o17 o o 22
* | 23 | 24 | | 20 | 24 |
* | | | | | |
* 3 o----o----o----o----o 5 3 o----o----o----o----o 10
* | 11 4| 12 | | 6 2| 13 |
* | | | | | |
* 15 o [0] o16 [1] o 17 7 o o o5 o o 12
* | 21 | 22 | | 8 | 14 |
* | | | | | |
* 0 o----o----o----o----o 2 0 o----o----o----o----o 9
* 9 1 10 4 1 11
*/
//verbose()
chk.PrintTitle("phi01")
// start simulation
analysis := NewFEM("data/phi01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 25)
chk.IntAssert(len(dom.Elems), 4)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 1)
chk.StrAssert(nod.Dofs[0].Key, "h")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{
0, 1, 4, 3, 9, 16, 11, 15, 21, 2, 5, 10, 17, 12, 22, 7, 6, 19, 13, 18, 23, 8, 20, 14, 24,
})
chk.Ints(tst, "eqs", eqs, []int{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
})
// check initial values
r := 0.25
chk.Scalar(tst, "h @ nod 4", 1e-17, dom.Sol.Y[2], -r)
chk.Scalar(tst, "h @ nod 8", 1e-17, dom.Sol.Y[21], math.Sqrt(2)/2.0-r)
for _, eq := range []int{5, 6, 13, 17} {
chk.Scalar(tst, io.Sf("h @ eq %d", eq), 1e-17, dom.Sol.Y[eq], 0)
}
}
func Test_p01a(tst *testing.T) {
/* this tests simulates seepage flow along a column
* by reducing the initial hydrostatic pressure at
* at the bottom of the column
*
* Nodes / Tags Equations
*
* 8 o----o----o 9 (-5) 22 o----o----o 21
* | 14 | | 24 |
* | | | |
* 21 o o o 22 (-6) 25 o o o 23
* | 26 | | 26 |
* | | | |
* 6 o----o----o 7 (-4) 16 o----o----o 15
* | 13 | | 18 |
* | | | |
* 19 | o o 20 (-6) 19 | o o 17
* | 25 | | 20 |
* | | | |
* 4 o----o----o 5 (-3) 10 o----o----o 9
* | 12 | | 12 |
* | | | |
* 17 o o o 18 (-6) 13 o o o 11
* | 24 | | 14 |
* | | | |
* 2 o----o----o 3 (-2) 3 o----o----o 2
* | 11 | | 6 |
* | | | |
* 15 o o o 16 (-6) 7 o o o 5
* | 23 | | 8 |
* | | | |
* 0 o----o----o 1 (-1) 0 o----o----o 1
* 10 4
*/
//verbose()
chk.PrintTitle("p01a")
// start simulation
analysis := NewFEM("data/p01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 27)
chk.IntAssert(len(dom.Elems), 4)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 1)
chk.StrAssert(nod.Dofs[0].Key, "pl")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{
0, 1, 3, 2, 10, 16, 11, 15, 23,
5, 4, 18, 12, 17, 24,
7, 6, 20, 13, 19, 25,
9, 8, 22, 14, 21, 26,
})
chk.Ints(tst, "eqs", eqs, utl.IntRange(27))
// check pmap
pmaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8},
{3, 2, 9, 10, 6, 11, 12, 13, 14},
{10, 9, 15, 16, 12, 17, 18, 19, 20},
{16, 15, 21, 22, 18, 23, 24, 25, 26},
}
for i, ele := range dom.Elems {
e := ele.(*ElemP)
io.Pforan("e%d.pmap = %v\n", e.Id(), e.Pmap)
chk.Ints(tst, "pmap", e.Pmap, pmaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 3)
var ct_pl_eqs []int // equations with pl prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pforan("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "pl":
ct_pl_eqs = append(ct_pl_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_pl_eqs)
chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{0, 1, 4})
// initial values @ nodes
io.Pforan("initial values @ nodes\n")
for _, nod := range dom.Nodes {
z := nod.Vert.C[1]
eq := nod.Dofs[0].Eq
pl := dom.Sol.Y[eq]
plC, _, _ := dom.HydSta.Calc(z)
chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, pl), 1e-17, pl, plC)
}
// intial values @ integration points
io.Pforan("initial values @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemP)
for idx, ip := range e.IpsElem {
s := e.States[idx]
z := e.Cell.Shp.IpRealCoords(e.X, ip)[1]
_, ρLC, _ := dom.HydSta.Calc(z)
chk.Scalar(tst, io.Sf("sl(@ %18g)= %18g", z, s.A_sl), 1e-17, s.A_sl, 1)
chk.Scalar(tst, io.Sf("ρL(@ %18g)= %18g", z, s.A_ρL), 1e-13, s.A_ρL, ρLC)
}
}
}