// adds element K to global Jacobian matrix Kb
func (o ElemUP) AddToKb(Kb *la.Triplet, sol *Solution, firstIt bool) (ok bool) {
// clear matrices
ndim := Global.Ndim
u_nverts := o.U.Shp.Nverts
p_nverts := o.P.Shp.Nverts
la.MatFill(o.P.Kpp, 0)
for i := 0; i < o.U.Nu; i++ {
for j := 0; j < o.P.Np; j++ {
o.Kup[i][j] = 0
o.Kpu[j][i] = 0
}
for j := 0; j < o.U.Nu; j++ {
o.U.K[i][j] = 0
}
}
if o.P.DoExtrap {
for i := 0; i < p_nverts; i++ {
o.P.ρl_ex[i] = 0
for j := 0; j < p_nverts; j++ {
o.P.dρldpl_ex[i][j] = 0
}
for j := 0; j < o.U.Nu; j++ {
o.dρldus_ex[i][j] = 0
}
}
}
// for each integration point
dc := Global.DynCoefs
var coef, plt, klr, ρL, Cl, divvs float64
var ρl, ρ, Cpl, Cvs, dρdpl, dpdpl, dCpldpl, dCvsdpl, dklrdpl, dCpldusM, dρldusM, dρdusM float64
var r, c int
for idx, ip := range o.U.IpsElem {
// interpolation functions, gradients and variables @ ip
if !o.ipvars(idx, sol) {
return
}
coef = o.U.Shp.J * ip.W
S := o.U.Shp.S
G := o.U.Shp.G
Sb := o.P.Shp.S
Gb := o.P.Shp.G
// axisymmetric case
radius := 1.0
if Global.Sim.Data.Axisym {
radius = o.U.Shp.AxisymGetRadius(o.U.X)
coef *= radius
}
// auxiliary
divvs = dc.α4*o.divus - o.U.divχs[idx] // divergence of Eq (35a) [1]
// tpm variables
plt = dc.β1*o.P.pl - o.P.ψl[idx] // Eq (35c) [1]
klr = o.P.Mdl.Cnd.Klr(o.P.States[idx].A_sl)
ρL = o.P.States[idx].A_ρL
Cl = o.P.Mdl.Cl
if LogErr(o.P.Mdl.CalcLs(o.P.res, o.P.States[idx], o.P.pl, o.divus, true), "AddToKb") {
return
}
ρl = o.P.res.A_ρl
ρ = o.P.res.A_ρ
Cpl = o.P.res.Cpl
Cvs = o.P.res.Cvs
dρdpl = o.P.res.Dρdpl
dpdpl = o.P.res.Dpdpl
dCpldpl = o.P.res.DCpldpl
dCvsdpl = o.P.res.DCvsdpl
dklrdpl = o.P.res.Dklrdpl
dCpldusM = o.P.res.DCpldusM
dρldusM = o.P.res.DρldusM
dρdusM = o.P.res.DρdusM
// Kpu, Kup and Kpp
for n := 0; n < p_nverts; n++ {
for j := 0; j < ndim; j++ {
// Kpu := ∂Rl^n/∂us^m and Kup := ∂Rus^m/∂pl^n; see Eq (47) of [1]
for m := 0; m < u_nverts; m++ {
c = j + m*ndim
// add ∂rlb/∂us^m: Eqs (A.3) and (A.6) of [1]
o.Kpu[n][c] += coef * Sb[n] * (dCpldusM*plt + dc.α4*Cvs) * G[m][j]
// add ∂(ρl.wl)/∂us^m: Eq (A.8) of [1]
for i := 0; i < ndim; i++ {
o.Kpu[n][c] += coef * Gb[n][i] * S[m] * dc.α1 * ρL * klr * o.P.Mdl.Klsat[i][j]
}
// add ∂rl/∂pl^n and ∂p/∂pl^n: Eqs (A.9) and (A.11) of [1]
o.Kup[c][n] += coef * (S[m]*Sb[n]*dρdpl*o.bs[j] - G[m][j]*Sb[n]*dpdpl)
// for seepage face
if o.P.DoExtrap {
o.dρldus_ex[n][c] += o.P.Emat[n][idx] * dρldusM * G[m][j]
}
}
// term in brackets in Eq (A.7) of [1]
o.P.tmp[j] = Sb[n]*dklrdpl*o.hl[j] - klr*(Sb[n]*Cl*o.bs[j]+Gb[n][j])
}
// Kpp := ∂Rl^m/∂pl^n; see Eq (47) of [1]
for m := 0; m < p_nverts; m++ {
// add ∂rlb/dpl^n: Eq (A.5) of [1]
o.P.Kpp[m][n] += coef * Sb[m] * Sb[n] * (dCpldpl*plt + dCvsdpl*divvs + dc.β1*Cpl)
// add ∂(ρl.wl)/∂us^m: Eq (A.7) of [1]
for i := 0; i < ndim; i++ {
for j := 0; j < ndim; j++ {
o.P.Kpp[m][n] -= coef * Gb[m][i] * o.P.Mdl.Klsat[i][j] * o.P.tmp[j]
}
}
// inner summation term in Eq (22) of [2]
if o.P.DoExtrap {
o.P.dρldpl_ex[m][n] += o.P.Emat[m][idx] * Cpl * Sb[n]
}
}
// Eq. (19) of [2]
if o.P.DoExtrap {
o.P.ρl_ex[n] += o.P.Emat[n][idx] * ρl
}
}
// Kuu: add ∂rub^m/∂us^n; see Eqs (47) and (A.10) of [1]
for m := 0; m < u_nverts; m++ {
for i := 0; i < ndim; i++ {
r = i + m*ndim
for n := 0; n < u_nverts; n++ {
for j := 0; j < ndim; j++ {
c = j + n*ndim
o.U.K[r][c] += coef * S[m] * (S[n]*dc.α1*ρ*tsr.It[i][j] + dρdusM*o.bs[i]*G[n][j])
}
}
}
}
// consistent tangent model matrix
if LogErr(o.U.MdlSmall.CalcD(o.U.D, o.U.States[idx], firstIt), "AddToKb") {
return
}
// Kuu: add stiffness term ∂(σe・G^m)/∂us^n
if o.U.UseB {
IpBmatrix(o.U.B, ndim, u_nverts, G, radius, S)
la.MatTrMulAdd3(o.U.K, coef, o.U.B, o.U.D, o.U.B) // K += coef * tr(B) * D * B
} else {
IpAddToKt(o.U.K, u_nverts, ndim, coef, G, o.U.D)
}
}
// contribution from natural boundary conditions
if o.P.HasSeep {
if !o.P.add_natbcs_to_jac(sol) {
return
}
if !o.add_natbcs_to_jac(sol) {
return
}
}
// add K to sparse matrix Kb
// _ _
// | Kuu Kup 0 |
// | Kpu Kpp Kpf |
// |_ Kfu Kfp Kff _|
//
for i, I := range o.P.Pmap {
for j, J := range o.P.Pmap {
Kb.Put(I, J, o.P.Kpp[i][j])
}
for j, J := range o.P.Fmap {
Kb.Put(I, J, o.P.Kpf[i][j])
Kb.Put(J, I, o.P.Kfp[j][i])
}
for j, J := range o.U.Umap {
Kb.Put(I, J, o.Kpu[i][j])
Kb.Put(J, I, o.Kup[j][i])
}
}
for i, I := range o.P.Fmap {
for j, J := range o.P.Fmap {
Kb.Put(I, J, o.P.Kff[i][j])
}
}
for i, I := range o.U.Umap {
for j, J := range o.U.Umap {
Kb.Put(I, J, o.U.K[i][j])
}
}
return true
}
// AddToKb adds element K to global Jacobian matrix Kb
func (o *ElemU) AddToKb(Kb *la.Triplet, sol *Solution, firstIt bool) (ok bool) {
// zero K matrix
la.MatFill(o.K, 0)
// for each integration point
dc := Global.DynCoefs
ndim := Global.Ndim
nverts := o.Shp.Nverts
for idx, ip := range o.IpsElem {
// interpolation functions, gradients and variables @ ip
if !o.ipvars(idx, sol) {
return
}
// check Jacobian
if o.Shp.J < 0 {
LogErrCond(true, "ElemU: eid=%d: Jacobian is negative = %g\n", o.Id(), o.Shp.J)
return
}
// auxiliary
coef := o.Shp.J * ip.W * o.Thickness
S := o.Shp.S
G := o.Shp.G
// consistent tangent model matrix
if LogErr(o.MdlSmall.CalcD(o.D, o.States[idx], firstIt), "AddToKb") {
return
}
// add contribution to consistent tangent matrix
if o.UseB {
radius := 1.0
if Global.Sim.Data.Axisym {
radius = o.Shp.AxisymGetRadius(o.X)
coef *= radius
}
IpBmatrix(o.B, ndim, nverts, G, radius, S)
la.MatTrMulAdd3(o.K, coef, o.B, o.D, o.B) // K += coef * tr(B) * D * B
} else {
IpAddToKt(o.K, nverts, ndim, coef, G, o.D)
}
// dynamic term
if !Global.Sim.Data.Steady {
for m := 0; m < nverts; m++ {
for i := 0; i < ndim; i++ {
r := i + m*ndim
for n := 0; n < nverts; n++ {
c := i + n*ndim
o.K[r][c] += coef * S[m] * S[n] * (o.Rho*dc.α1 + o.Cdam*dc.α4)
}
}
}
}
}
// add K to sparse matrix Kb
for i, I := range o.Umap {
for j, J := range o.Umap {
Kb.Put(I, J, o.K[i][j])
}
}
return true
}
// AddToKb adds element K to global Jacobian matrix Kb
func (o *ElemU) AddToKb(Kb *la.Triplet, sol *Solution, firstIt bool) (err error) {
// zero K matrix
la.MatFill(o.K, 0)
// for each integration point
nverts := o.Cell.Shp.Nverts
for idx, ip := range o.IpsElem {
// interpolation functions, gradients and variables @ ip
err = o.ipvars(idx, sol)
if err != nil {
return
}
// check Jacobian
if o.Cell.Shp.J < 0 {
return chk.Err("ElemU: eid=%d: Jacobian is negative = %g\n", o.Id(), o.Cell.Shp.J)
}
// auxiliary
coef := o.Cell.Shp.J * ip[3] * o.Thickness
S := o.Cell.Shp.S
G := o.Cell.Shp.G
// consistent tangent model matrix
err = o.MdlSmall.CalcD(o.D, o.States[idx], firstIt)
if err != nil {
return
}
// add contribution to consistent tangent matrix
if o.UseB {
radius := 1.0
if sol.Axisym {
radius = o.Cell.Shp.AxisymGetRadius(o.X)
coef *= radius
}
IpBmatrix(o.B, o.Ndim, nverts, G, radius, S, sol.Axisym)
la.MatTrMulAdd3(o.K, coef, o.B, o.D, o.B) // K += coef * tr(B) * D * B
} else {
IpAddToKt(o.K, nverts, o.Ndim, coef, G, o.D)
}
// dynamic term
if !sol.Steady {
α1 := sol.DynCfs.α1
α4 := sol.DynCfs.α4
for m := 0; m < nverts; m++ {
for i := 0; i < o.Ndim; i++ {
r := i + m*o.Ndim
for n := 0; n < nverts; n++ {
c := i + n*o.Ndim
o.K[r][c] += coef * S[m] * S[n] * (o.Rho*α1 + o.Cdam*α4)
}
}
}
}
}
// add Ks to sparse matrix Kb
switch {
case o.HasContact:
err = o.contact_add_to_jac(Kb, sol)
case o.Xfem:
err = o.xfem_add_to_jac(Kb, sol)
default:
for i, I := range o.Umap {
for j, J := range o.Umap {
Kb.Put(I, J, o.K[i][j])
}
}
}
return
}