func (o *RichardsonExtrap) Init(d *Domain, Dt fun.Func) {
// backup variables
o.Y_big = make([]float64, d.Ny)
// auxiliary variables
o.nsteps = 0
o.naccept = 0
o.nreject = 0
o.ngustaf = 0
o.reject = false
o.laststep = false
// divergence control
o.ndiverg = 0
o.prevdiv = false
o.diverging = false
// time loop
o.Δt = Dt.F(0, nil)
o.Δtcpy = o.Δt
}
func (o *RichardsonExtrap) Run(d *Domain, s *Summary, DtOut fun.Func, time *float64, tf, tout float64, tidx *int) (ok bool) {
// stat
defer func() {
if Global.Root {
log.Printf("total number of steps = %d\n", o.nsteps)
log.Printf("number of accepted steps = %d\n", o.naccept)
log.Printf("number of rejected steps = %d\n", o.nreject)
log.Printf("number of Gustaffson's corrections = %d\n", o.ngustaf)
}
}()
// constants
atol := Global.Sim.Solver.REatol
rtol := Global.Sim.Solver.RErtol
mmin := Global.Sim.Solver.REmmin
mmax := Global.Sim.Solver.REmmax
mfac := Global.Sim.Solver.REmfac
// time loop
t := *time
defer func() { *time = t }()
var ΔtOld, rerrOld float64
for t < tf {
// check for continued divergence
if LogErrCond(o.ndiverg >= Global.Sim.Solver.NdvgMax, "continuous divergence after %d steps reached", o.ndiverg) {
return
}
// check time increment
if LogErrCond(o.Δt < Global.Sim.Solver.DtMin, "Δt increment is too small: %g < %g", o.Δt, Global.Sim.Solver.DtMin) {
return
}
// compute dynamic coefficients
if LogErr(Global.DynCoefs.CalcBoth(o.Δt), "cannot compute dynamic coefficients") {
return
}
// check for maximum number of substeps
o.nsteps += 1
if LogErrCond(o.nsteps >= Global.Sim.Solver.REnssmax, "RE: max number of steps reached: %d", o.nsteps) {
return
}
// backup domain
d.backup()
// single step with Δt
d.Sol.T = t + o.Δt
o.diverging, ok = run_iterations(t+o.Δt, o.Δt, d, s)
if !ok {
return
}
if Global.Sim.Solver.DvgCtrl {
if o.divergence_control(d, "big step") {
continue
}
}
// save intermediate state
for i := 0; i < d.Ny; i++ {
o.Y_big[i] = d.Sol.Y[i]
}
// restore initial state
d.restore()
// 1st halved step
d.Sol.T = t + o.Δt/2.0
o.diverging, ok = run_iterations(t+o.Δt/2.0, o.Δt/2.0, d, s)
if !ok {
break
}
if Global.Sim.Solver.DvgCtrl {
if o.divergence_control(d, "1st half step") {
continue
}
}
// 2nd halved step
d.Sol.T = t + o.Δt
o.diverging, ok = run_iterations(t+o.Δt, o.Δt/2.0, d, s)
if !ok {
break
}
if Global.Sim.Solver.DvgCtrl {
if o.divergence_control(d, "2nd half step") {
continue
}
}
// Richardson's extrapolation error
rerr := la.VecRmsError(d.Sol.Y, o.Y_big, atol, rtol, d.Sol.Y) / 3.0
// step size change
m := min(mmax, max(mmin, mfac*math.Pow(1.0/rerr, 1.0/2.0)))
ΔtNew := m * o.Δt
// accepted
if rerr < 1.0 {
// update variables
o.naccept += 1
t += o.Δt
d.Sol.T = t
// output
if Global.Verbose {
if !Global.Sim.Data.ShowR && !Global.Debug {
io.PfWhite("%30.15f\r", t)
}
}
//if true {
if t >= tout || o.laststep {
s.OutTimes = append(s.OutTimes, t)
if !d.Out(*tidx) {
return
}
tout += DtOut.F(t, nil)
*tidx += 1
}
// reached final time
if o.laststep {
if Global.Verbose {
io.Pfgreen("\n\nRichardson extrapolation succeeded\n")
}
return true
}
// predictive controller of Gustafsson
if !Global.Sim.Solver.REnogus {
if o.naccept > 1 {
m = mfac * (o.Δt / ΔtOld) * math.Sqrt(1.0/rerr) * math.Sqrt(rerrOld/rerr)
if m*o.Δt < ΔtNew {
o.ngustaf += 1
}
ΔtNew = min(ΔtNew, m*o.Δt)
}
ΔtOld = o.Δt
rerrOld = max(0.9, rerr) // 1e-2
}
// next step size
if o.reject { // do not alow Δt to grow if previous was a reject
ΔtNew = min(o.Δt, ΔtNew)
}
o.reject = false
o.Δt = ΔtNew
if t+ΔtNew-tf >= 0.0 {
o.laststep = true
o.Δt = tf - t
}
// rejected
} else {
// restore state
d.restore()
// set flags
o.nreject += 1
o.reject = true
o.laststep = false
// next step size
o.Δt = ΔtNew
if t+o.Δt > tf {
o.Δt = tf - t
}
}
}
return true
}
func (o *SolverImplicit) Run(tf float64, dtFunc, dtoFunc fun.Func, verbose bool, dbgKb DebugKb_t) (err error) {
// auxiliary
md := 1.0 // time step multiplier if divergence control is on
ndiverg := 0 // number of steps diverging
// control
t := o.doms[0].Sol.T
dat := o.doms[0].Sim.Solver
tout := t + dtoFunc.F(t, nil)
steady := o.doms[0].Sim.Data.Steady
// first output
if o.sum != nil {
err = o.sum.SaveDomains(t, o.doms, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
// time loop
var Δt float64
var lasttimestep bool
for t < tf {
// check for continued divergence
if ndiverg >= dat.NdvgMax {
return chk.Err("continuous divergence after %d steps reached", ndiverg)
}
// time increment
Δt = dtFunc.F(t, nil) * md
if t+Δt >= tf {
lasttimestep = true
}
if Δt < dat.DtMin {
if md < 1 {
return chk.Err("Δt increment is too small: %g < %g", Δt, dat.DtMin)
}
}
t += Δt
// dynamic coefficients
if !steady {
err = o.dc.CalcBoth(Δt)
if err != nil {
return chk.Err("cannot compute dynamic coefficients")
}
}
// message
if verbose {
if !dat.ShowR {
io.PfWhite("%30.15f\r", t)
}
}
// for all domains
docontinue := false
for _, d := range o.doms {
// backup solution if divergence control is on
if dat.DvgCtrl {
d.backup()
}
// run iterations
d.Sol.T = t
d.Sol.Dt = Δt
diverging, err := run_iterations(t, Δt, d, o.dc, o.sum, dbgKb)
if err != nil {
return chk.Err("run_iterations failed:\n%v", err)
}
// restore solution and reduce time step if divergence control is on
if dat.DvgCtrl {
if diverging {
if verbose {
io.Pfred(". . . iterations diverging (%2d) . . .\n", ndiverg+1)
}
d.restore()
t -= Δt
d.Sol.T = t
md *= 0.5
ndiverg += 1
docontinue = true
break
}
ndiverg = 0
md = 1.0
}
}
if docontinue {
continue
}
// perform output
if t >= tout || lasttimestep {
if o.sum != nil {
err = o.sum.SaveDomains(t, o.doms, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
tout += dtoFunc.F(t, nil)
}
}
return
}
func (o *RichardsonExtrap) Run(tf float64, dtFunc, dtoFunc fun.Func, verbose bool, dbgKb DebugKb_t) (err error) {
// constants
dat := o.doms[0].Sim.Solver
atol := dat.REatol
rtol := dat.RErtol
mmin := dat.REmmin
mmax := dat.REmmax
mfac := dat.REmfac
// control
t := o.doms[0].Sol.T
tout := t + dtoFunc.F(t, nil)
steady := o.doms[0].Sim.Data.Steady
// first output
if o.sum != nil {
err = o.sum.SaveDomains(t, o.doms, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
// domain and variables
d := o.doms[0]
o.Y_big = make([]float64, d.Ny)
// time loop
o.Δt = dtFunc.F(t, nil)
o.Δtcpy = o.Δt
var ΔtOld, rerrOld float64
for t < tf {
// check for continued divergence
if o.ndiverg >= dat.NdvgMax {
return chk.Err("continuous divergence after %d steps reached", o.ndiverg)
}
// check time increment
if o.Δt < dat.DtMin {
return chk.Err("Δt increment is too small: %g < %g", o.Δt, dat.DtMin)
}
// dynamic coefficients
if !steady {
err = o.dc.CalcBoth(o.Δt)
if err != nil {
return chk.Err("cannot compute dynamic coefficients:\n%v", err)
}
}
// check for maximum number of substeps
o.nsteps += 1
if o.nsteps >= dat.REnssmax {
return chk.Err("RE: max number of steps reached: %d", o.nsteps)
}
// backup domain
d.backup()
// single step with Δt
d.Sol.T = t + o.Δt
d.Sol.Dt = o.Δt
o.diverging, err = run_iterations(t+o.Δt, o.Δt, d, o.dc, o.sum, dbgKb)
if err != nil {
return chk.Err("single step with Δt: run_iterations failed:\n%v", err)
}
if dat.DvgCtrl {
if o.divergence_control(d, "big step", verbose) {
continue
}
}
// save intermediate state
for i := 0; i < d.Ny; i++ {
o.Y_big[i] = d.Sol.Y[i]
}
// restore initial state
d.restore()
// 1st halved step
d.Sol.T = t + o.Δt/2.0
d.Sol.Dt = o.Δt / 2.0
o.diverging, err = run_iterations(t+o.Δt/2.0, o.Δt/2.0, d, o.dc, o.sum, dbgKb)
if err != nil {
return chk.Err("1st halved step: run_iterations failed:\n%v", err)
}
if dat.DvgCtrl {
if o.divergence_control(d, "1st half step", verbose) {
continue
}
}
// 2nd halved step
d.Sol.T = t + o.Δt
d.Sol.Dt = o.Δt
o.diverging, err = run_iterations(t+o.Δt, o.Δt/2.0, d, o.dc, o.sum, dbgKb)
if err != nil {
return chk.Err("2nd halved step: run_iterations failed:\n%v", err)
}
if dat.DvgCtrl {
if o.divergence_control(d, "2nd half step", verbose) {
continue
}
}
// Richardson's extrapolation error
rerr := la.VecRmsError(d.Sol.Y, o.Y_big, atol, rtol, d.Sol.Y) / 3.0
// step size change
m := utl.Min(mmax, utl.Max(mmin, mfac*math.Pow(1.0/rerr, 1.0/2.0)))
ΔtNew := m * o.Δt
// accepted
if rerr < 1.0 {
// update variables
o.naccept += 1
t += o.Δt
d.Sol.T = t
// output
if verbose {
if !dat.ShowR {
io.PfWhite("%30.15f\r", t)
}
}
if t >= tout || o.laststep {
if o.sum != nil {
err = o.sum.SaveDomains(t, o.doms, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
tout += dtoFunc.F(t, nil)
}
// reached final time
if o.laststep {
if verbose {
io.Pfgreen("\n\nRichardson extrapolation succeeded\n")
}
return
}
// predictive controller of Gustafsson
if !dat.REnogus {
if o.naccept > 1 {
m = mfac * (o.Δt / ΔtOld) * math.Sqrt(1.0/rerr) * math.Sqrt(rerrOld/rerr)
if m*o.Δt < ΔtNew {
o.ngustaf += 1
}
ΔtNew = utl.Min(ΔtNew, m*o.Δt)
}
ΔtOld = o.Δt
rerrOld = utl.Max(0.9, rerr) // 1e-2
}
// next step size
if o.reject { // do not alow Δt to grow if previous was a reject
ΔtNew = utl.Min(o.Δt, ΔtNew)
}
o.reject = false
o.Δt = ΔtNew
if t+ΔtNew-tf >= 0.0 {
o.laststep = true
o.Δt = tf - t
}
// rejected
} else {
// restore state
d.restore()
// set flags
o.nreject += 1
o.reject = true
o.laststep = false
// next step size
o.Δt = ΔtNew
if t+o.Δt > tf {
o.Δt = tf - t
}
}
}
return
}
func (o *SolverLinearImplicit) Run(tf float64, dtFunc, dtoFunc fun.Func, verbose bool, notused DebugKb_t) (err error) {
// control
t := o.dom.Sol.T
tout := t + dtoFunc.F(t, nil)
steady := o.dom.Sim.Data.Steady
// first output
if o.sum != nil {
err = o.sum.SaveDomains(t, []*Domain{o.dom}, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
// auxiliary variables
Y := o.dom.Sol.Y
ψ := o.dom.Sol.Psi
ζ := o.dom.Sol.Zet
χ := o.dom.Sol.Chi
dydt := o.dom.Sol.Dydt
d2ydt2 := o.dom.Sol.D2ydt2
// time loop
first := true
var Δt float64
var lasttimestep bool
for t < tf {
// time increment
Δt = dtFunc.F(t, nil)
if t+Δt >= tf {
lasttimestep = true
}
t += Δt
// update time variable in solution array
o.dom.Sol.T = t
o.dom.Sol.Dt = Δt
// dynamic coefficients
if !steady {
err = o.dc.CalcBoth(Δt)
if err != nil {
return chk.Err("cannot compute dynamic coefficients")
}
}
// message
if verbose {
io.PfWhite("%30.15f\r", t)
}
// calculate global starred vectors and interpolate starred variables from nodes to integration points
if !steady {
// compute starred vectors
for _, I := range o.dom.T1eqs {
ψ[I] = Y[I] - o.dom.Sol.ΔY[I]
}
for _, I := range o.dom.T2eqs {
ζ[I] = Y[I]
χ[I] = Y[I]
}
// set internal starred variables
for _, e := range o.dom.Elems {
err = e.InterpStarVars(o.dom.Sol)
if err != nil {
err = chk.Err("cannot compute starred variables:\n%v", err)
return
}
}
}
// solve linear problem
err := solve_linear_problem(t, o.dom, o.dc, o.sum, first)
if err != nil {
return chk.Err("solve_linear_problem failed:\n%v", err)
}
first = false
// update velocity and acceleration
if !steady {
for _, I := range o.dom.T1eqs {
dydt[I] = Y[I] - ψ[I]
}
for _, I := range o.dom.T2eqs {
dydt[I] = o.dc.α4*Y[I] - χ[I]
d2ydt2[I] = o.dc.α1*Y[I] - ζ[I]
}
}
// perform output
if t >= tout || lasttimestep {
if o.sum != nil {
err = o.sum.SaveDomains(t, []*Domain{o.dom}, false)
if err != nil {
return chk.Err("cannot save results:\n%v", err)
}
}
tout += dtoFunc.F(t, nil)
}
}
return
}