// Print prints coefficients
func (o *DynCoefs) Print() {
io.Pfgrey("θ=%v, θ1=%v, θ2=%v, α=%v\n", o.θ, o.θ1, o.θ2, o.α)
io.Pfgrey("HHT=%v\n", o.HHT)
io.Pfgrey("β1=%v, β2=%v\n", o.β1, o.β2)
io.Pfgrey("α1=%v, α2=%v, α3=%v, α4=%v, α5=%v, α6=%v\n", o.α1, o.α2, o.α3, o.α4, o.α5, o.α6)
io.Pfgrey("α7=%v, α8=%v\n", o.α7, o.α8)
}
// msg prints information on residuals
func (o *NlSolver) msg(typ string, it int, Ldx, fx_max float64, first, last bool) {
if first {
io.Pfpink("\n%4s%23s%23s\n", "it", "Ldx", "fx_max")
io.Pfpink("%4s%23s%23s\n", "", io.Sf("(%7.1e)", o.fnewt), io.Sf("(%7.1e)", o.ftol))
return
}
io.Pfyel("%4d%23.15e%23.15e\n", it, Ldx, fx_max)
if last {
io.Pfgrey(". . . converged with %s. nit=%d, nFeval=%d, nJeval=%d\n", typ, it, o.NFeval, o.NJeval)
}
}
// KrefineN return a new Nurbs with each span divided into ndiv parts = [2, 3, ...]
func (o *Nurbs) KrefineN(ndiv int, hughesEtAlPaper bool) *Nurbs {
X := make([][]float64, o.gnd)
if hughesEtAlPaper {
elems := o.Elements()
switch o.gnd {
case 2:
for _, e := range elems {
umin, umax := o.b[0].T[e[0]], o.b[0].T[e[1]]
vmin, vmax := o.b[1].T[e[2]], o.b[1].T[e[3]]
xa := o.Point([]float64{umin, vmin})
xb := o.Point([]float64{umax, vmin})
xc := []float64{(xa[0] + xb[0]) / 2.0, (xa[1] + xb[1]) / 2.0}
io.Pf("xa = %v\n", xa)
io.Pf("xb = %v\n", xb)
io.Pf("xc = %v\n", xc)
xa = o.Point([]float64{umin, vmax})
xb = o.Point([]float64{umax, vmax})
xc = []float64{(xa[0] + xb[0]) / 2.0, (xa[1] + xb[1]) / 2.0}
io.Pfpink("xa, xb, xc = %v, %v, %v\n", xa, xb, xc)
chk.Panic("KrefineN with hughesEtAlPaper==true is not implemented in 2D yet")
}
case 3:
chk.Panic("KrefineN with hughesEtAlPaper==true is not implemented in 3D yet")
}
io.Pfgrey("KrefineN with hughesEtAlPaper==true => not implemented yet\n")
return nil
} else {
for d := 0; d < o.gnd; d++ {
nspans := o.b[d].m - 2*o.p[d] - 1
nnewk := nspans * (ndiv - 1)
X[d] = make([]float64, nnewk)
k := 0
for i := 0; i < nspans; i++ {
umin, umax := o.b[d].T[o.p[d]+i], o.b[d].T[o.p[d]+i+1]
du := (umax - umin) / float64(ndiv)
for j := 1; j < ndiv; j++ {
X[d][k] = umin + du*float64(j)
k += 1
}
}
}
}
return o.Krefine(X)
}
// backward-Euler
func bweuler_step(o *ODE, y []float64, x float64, args ...interface{}) (rerr float64, err error) {
// new x
x += o.h
// previous y
la.VecCopy(o.v[0], 1, y) // v := y_old
// iterations
var rmsnr float64 // rms norm of residual
var it int
for it = 0; it < o.NmaxIt; it++ {
// max iterations ?
o.nit = it + 1
if o.nit > o.nitmax {
o.nitmax = o.nit
}
// calculate f @ update y
o.nfeval += 1
err = o.fcn(o.f[0], x, y, args...)
if err != nil {
return
}
// calculate residual
rmsnr = 0.0
for i := 0; i < o.ndim; i++ {
o.w[0][i] = y[i] - o.v[0][i] - o.h*o.f[0][i] // w := residual
if o.UseRmsNorm {
rmsnr += math.Pow(o.w[0][i]/o.scal[i], 2.0)
} else {
rmsnr += o.w[0][i] * o.w[0][i]
}
}
if o.UseRmsNorm {
rmsnr = math.Sqrt(rmsnr / float64(o.ndim))
} else {
rmsnr = math.Sqrt(rmsnr)
}
if o.Verbose {
io.Pfgrey(" residual = %10.5e (tol = %10.5e)\n", rmsnr, o.fnewt)
}
// converged
if rmsnr < o.fnewt {
break
}
// Jacobian matrix
if o.doinit || !o.CteTg {
o.njeval += 1
// calculate Jacobian
if o.jac == nil { // numerical
err = num.Jacobian(&o.dfdyT, func(fy, yy []float64) (e error) {
e = o.fcn(fy, x, yy, args...)
return
}, y, o.f[0], o.δw[0], o.Distr) // δw works here as workspace variable
} else { // analytical
err = o.jac(&o.dfdyT, x, y, args...)
}
if err != nil {
return
}
// debug
//if true {
//io.Pfblue2("J = %v\n", o.dfdyT.ToMatrix(nil).ToDense()[0])
//}
if o.doinit {
o.rctriR = new(la.Triplet)
o.rctriR.Init(o.ndim, o.ndim, o.mTri.Len()+o.dfdyT.Len())
}
// calculate drdy matrix
la.SpTriAdd(o.rctriR, 1, o.mTri, -o.h, &o.dfdyT) // rctriR := I - h * dfdy
//la.PrintMat("rcmat", o.rctriR.ToMatrix(nil).ToDense(), "%8.3f", false)
// initialise linear solver
if o.doinit {
err = o.lsolR.InitR(o.rctriR, false, false, false)
if err != nil {
return
}
}
// perform factorisation
o.ndecomp += 1
o.lsolR.Fact()
}
// solve linear system
o.nlinsol += 1
o.lsolR.SolveR(o.δw[0], o.w[0], false) // δw := inv(rcmat) * residual
// update y
for i := 0; i < o.ndim; i++ {
y[i] -= o.δw[0][i]
}
}
// did not converge
if it == o.NmaxIt-1 {
chk.Panic("bweuler_step failed with it = %d", it)
}
return 1e+20, err // must not be used with automatic substepping
}
// Run computes β starting witn an initial guess
func (o *ReliabFORM) Run(βtrial float64, verbose bool, args ...interface{}) (β float64, μ, σ, x []float64) {
// initial random variables
β = βtrial
nx := len(o.μ)
μ = make([]float64, nx) // mean values (equivalent normal value)
σ = make([]float64, nx) // deviation values (equivalent normal value)
x = make([]float64, nx) // current vector of random variables defining min(β)
for i := 0; i < nx; i++ {
μ[i] = o.μ[i]
σ[i] = o.σ[i]
x[i] = o.μ[i]
}
// lognormal distribution structure
var lnd DistLogNormal
// has lognormal random variable?
haslrv := false
for _, found := range o.lrv {
if found {
haslrv = true
break
}
}
// function to compute β with x-constant
// gβ(β) = g(μ - β・A・σ) = 0
var err error
gβfcn := func(fy, y []float64) error {
βtmp := y[0]
for i := 0; i < nx; i++ {
o.xtmp[i] = μ[i] - βtmp*o.α[i]*σ[i]
}
fy[0], err = o.gfcn(o.xtmp, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", o.xtmp, err)
}
return nil
}
// derivative of gβ w.r.t β
hβfcn := func(dfdy [][]float64, y []float64) error {
βtmp := y[0]
for i := 0; i < nx; i++ {
o.xtmp[i] = μ[i] - βtmp*o.α[i]*σ[i]
}
err = o.hfcn(o.dgdx, o.xtmp, args)
if err != nil {
chk.Panic("cannot compute hfcn(%v):\n%v", o.xtmp, err)
}
dfdy[0][0] = 0
for i := 0; i < nx; i++ {
dfdy[0][0] -= o.dgdx[i] * o.α[i] * σ[i]
}
return nil
}
// nonlinear solver with y[0] = β
// solving: gβ(β) = g(μ - β・A・σ) = 0
var nls num.NlSolver
nls.Init(1, gβfcn, nil, hβfcn, true, false, nil)
defer nls.Clean()
// message
if verbose {
io.Pf("\n%s", io.StrThickLine(60))
}
// plotting
plot := o.PlotFnk != ""
if nx != 2 {
plot = false
}
if plot {
if o.PlotNp < 3 {
o.PlotNp = 41
}
var umin, umax, vmin, vmax float64
if o.PlotCf < 1 {
o.PlotCf = 2
}
if len(o.PlotUrange) == 0 {
umin, umax = μ[0]-o.PlotCf*μ[0], μ[0]+o.PlotCf*μ[0]
vmin, vmax = μ[1]-o.PlotCf*μ[1], μ[1]+o.PlotCf*μ[1]
} else {
chk.IntAssert(len(o.PlotUrange), 2)
chk.IntAssert(len(o.PlotVrange), 2)
umin, umax = o.PlotUrange[0], o.PlotUrange[1]
vmin, vmax = o.PlotVrange[0], o.PlotVrange[1]
}
o.PlotU, o.PlotV = utl.MeshGrid2D(umin, umax, vmin, vmax, o.PlotNp, o.PlotNp)
o.PlotZ = la.MatAlloc(o.PlotNp, o.PlotNp)
plt.SetForEps(0.8, 300)
for i := 0; i < o.PlotNp; i++ {
for j := 0; j < o.PlotNp; j++ {
o.xtmp[0] = o.PlotU[i][j]
o.xtmp[1] = o.PlotV[i][j]
o.PlotZ[i][j], err = o.gfcn(o.xtmp, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
}
}
plt.Contour(o.PlotU, o.PlotV, o.PlotZ, "")
plt.ContourSimple(o.PlotU, o.PlotV, o.PlotZ, true, 8, "levels=[0], colors=['yellow']")
plt.PlotOne(x[0], x[1], "'ro', label='initial'")
}
// iterations to find β
var dat VarData
B := []float64{β}
itB := 0
for itB = 0; itB < o.NmaxItB; itB++ {
// message
if verbose {
gx, err := o.gfcn(x, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
io.Pf("%s itB=%d β=%g g=%g\n", io.StrThinLine(60), itB, β, gx)
}
// plot
if plot {
plt.PlotOne(x[0], x[1], "'r.'")
}
// compute direction cosines
itA := 0
for itA = 0; itA < o.NmaxItA; itA++ {
// has lognormal random variable (lrv)
if haslrv {
// find equivalent normal mean and std deviation for lognormal variables
for i := 0; i < nx; i++ {
if o.lrv[i] {
// set distribution
dat.M, dat.S = o.μ[i], o.σ[i]
lnd.Init(&dat)
// update μ and σ
fx := lnd.Pdf(x[i])
Φinvx := (math.Log(x[i]) - lnd.M) / lnd.S
φx := math.Exp(-Φinvx*Φinvx/2.0) / math.Sqrt2 / math.SqrtPi
σ[i] = φx / fx
μ[i] = x[i] - Φinvx*σ[i]
}
}
}
// compute direction cosines
err = o.hfcn(o.dgdx, x, args)
if err != nil {
chk.Panic("cannot compute hfcn(%v):\n%v", x, err)
}
den := 0.0
for i := 0; i < nx; i++ {
den += math.Pow(o.dgdx[i]*σ[i], 2.0)
}
den = math.Sqrt(den)
αerr := 0.0 // difference on α
for i := 0; i < nx; i++ {
αnew := o.dgdx[i] * σ[i] / den
αerr += math.Pow(αnew-o.α[i], 2.0)
o.α[i] = αnew
}
αerr = math.Sqrt(αerr)
// message
if verbose {
io.Pf(" itA=%d\n", itA)
io.Pf("%12s%12s%12s%12s\n", "x", "μ", "σ", "α")
for i := 0; i < nx; i++ {
io.Pf("%12.3f%12.3f%12.3f%12.3f\n", x[i], μ[i], σ[i], o.α[i])
}
}
// update x-star
for i := 0; i < nx; i++ {
x[i] = μ[i] - β*o.α[i]*σ[i]
}
// check convergence on α
if itA > 1 && αerr < o.TolA {
if verbose {
io.Pfgrey(". . . converged on α with αerr=%g . . .\n", αerr)
}
break
}
}
// failed to converge on α
if itA == o.NmaxItA {
chk.Panic("failed to convege on α")
}
// compute new β
B[0] = β
nls.Solve(B, o.NlsSilent)
βerr := math.Abs(B[0] - β)
β = B[0]
if o.NlsCheckJ {
nls.CheckJ(B, o.NlsCheckJtol, true, false)
}
// update x-star
for i := 0; i < nx; i++ {
x[i] = μ[i] - β*o.α[i]*σ[i]
}
// check convergence on β
if βerr < o.TolB {
if verbose {
io.Pfgrey2(". . . converged on β with βerr=%g . . .\n", βerr)
}
break
}
}
// failed to converge on β
if itB == o.NmaxItB {
chk.Panic("failed to converge on β")
}
// message
if verbose {
gx, err := o.gfcn(x, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
io.Pfgreen("x = %v\n", x)
io.Pfgreen("g = %v\n", gx)
io.PfGreen("β = %v\n", β)
}
// plot
if plot {
plt.Gll("$x_0$", "$x_1$", "")
plt.Cross("")
plt.SaveD("/tmp/gosl", "fig_form_"+o.PlotFnk+".eps")
}
return
}
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
}
// Update updates state
// pl and pg are updated (new) values
func (o Model) Update(s *State, Δpl, Δpg, pl, pg float64) (err error) {
// auxiliary variables
slmin := o.Lrm.SlMin()
Δpc := Δpg - Δpl
wet := Δpc < 0
pl0 := pl - Δpl
pg0 := pg - Δpg
pc0 := pg0 - pl0
sl0 := s.A_sl
pc := pc0 + Δpc
sl := sl0
// update liquid saturation
if pc <= 0.0 {
sl = 1 // full liquid saturation if capillary pressure is ineffective
} else if o.nonrateLrm != nil && !o.AllBE {
sl = o.nonrateLrm.Sl(pc) // handle simple retention models
} else { // unsaturated case with rate-type model
// trial liquid saturation update
fA, e := o.Lrm.Cc(pc0, sl0, wet)
if e != nil {
return e
}
if o.MEtrial {
slFE := sl0 + Δpc*fA
fB, e := o.Lrm.Cc(pc, slFE, wet)
if e != nil {
return e
}
sl += 0.5 * Δpc * (fA + fB)
} else {
sl += Δpc * fA
}
// fix trial sl out-of-range values
if sl < slmin {
sl = slmin
}
if sl > 1 {
sl = 1
}
// message
if o.ShowR {
io.PfYel("%6s%18s%18s%18s%18s%8s\n", "it", "Cc", "sl", "δsl", "r", "ex(r)")
}
// backward-Euler update
var f, r, J, δsl float64
var it int
for it = 0; it < o.NmaxIt; it++ {
f, err = o.Lrm.Cc(pc, sl, wet)
if err != nil {
return
}
r = sl - sl0 - Δpc*f
if o.ShowR {
io.Pfyel("%6d%18.14f%18.14f%18.14f%18.10e%8d\n", it, f, sl, δsl, r, utl.Expon(r))
}
if math.Abs(r) < o.Itol {
break
}
J, err = o.Lrm.J(pc, sl, wet)
if err != nil {
return
}
δsl = -r / (1.0 - Δpc*J)
sl += δsl
if math.IsNaN(sl) {
return chk.Err("NaN found: Δpc=%v f=%v r=%v J=%v sl=%v\n", Δpc, f, r, J, sl)
}
}
// message
if o.ShowR {
io.Pfgrey(" pc0=%.6f sl0=%.6f Δpl=%.6f Δpg=%.6f Δpc=%.6f\n", pc0, sl0, Δpl, Δpg, Δpc)
io.Pfgrey(" converged with %d iterations\n", it)
}
// check convergence
if it == o.NmaxIt {
return chk.Err("saturation update failed after %d iterations\n", it)
}
}
// check results
if pc < 0 && sl < 1 {
return chk.Err("inconsistent results: saturation must be equal to one when the capillary pressure is ineffective. pc = %g < 0 and sl = %g < 1 is incorrect", pc, sl)
}
if sl < slmin {
return chk.Err("inconsistent results: saturation must be greater than minimum saturation. sl = %g < %g is incorrect", sl, slmin)
}
// set state
s.A_sl = sl // 2
s.A_ρL += o.Cl * Δpl // 3
s.A_ρG += o.Cg * Δpg // 4
s.A_Δpc = Δpc // 5
s.A_wet = wet // 6
return
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
io.PfYel("\nTest MPI 01\n")
}
if mpi.Size() != 3 {
chk.Panic("this test needs 3 processors")
}
n := 11
x := make([]float64, n)
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*n)/sz, ((id+1)*n)/sz
for i := start; i < endp1; i++ {
x[i] = float64(i)
}
// Barrier
mpi.Barrier()
io.Pfgrey("x @ proc # %d = %v\n", id, x)
// SumToRoot
r := make([]float64, n)
mpi.SumToRoot(r, x)
var tst testing.T
if id == 0 {
chk.Vector(&tst, fmt.Sprintf("SumToRoot: r @ proc # %d", id), 1e-17, r, []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
} else {
chk.Vector(&tst, fmt.Sprintf("SumToRoot: r @ proc # %d", id), 1e-17, r, make([]float64, n))
}
// BcastFromRoot
r[0] = 666
mpi.BcastFromRoot(r)
chk.Vector(&tst, fmt.Sprintf("BcastFromRoot: r @ proc # %d", id), 1e-17, r, []float64{666, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
// AllReduceSum
setslice(x)
w := make([]float64, n)
mpi.AllReduceSum(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceSum: w @ proc # %d", id), 1e-17, w, []float64{110, 110, 110, 1021, 1021, 1021, 2032, 2032, 2032, 3043, 3043})
// AllReduceSumAdd
setslice(x)
y := []float64{-1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000}
mpi.AllReduceSumAdd(y, x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceSumAdd: y @ proc # %d", id), 1e-17, y, []float64{-890, -890, -890, 21, 21, 21, 1032, 1032, 1032, 2043, 2043})
// AllReduceMin
setslice(x)
mpi.AllReduceMin(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceMin: x @ proc # %d", id), 1e-17, x, []float64{0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3})
// AllReduceMax
setslice(x)
mpi.AllReduceMax(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceMax: x @ proc # %d", id), 1e-17, x, []float64{100, 100, 100, 1000, 1000, 1000, 2000, 2000, 2000, 3000, 3000})
}