conv_rates_static.lua File Reference

Functions
function util rates static	compute (ConvRateSetup)
function util rates static StdLabel	MeasLatexP (disc, p)
function util rates static StdLabel	MeasLatexQ (disc, p)
function util rates static StdLabel	MeasPdfP (disc, p)
function util rates static StdLabel	MeasPdfQ (disc, p)
function util rates static	NoMaxLevelPadding (p)
function util rates static	NoMinLevelPadding (p)
function util rates static	replot (gpOptions, file)
function util rates static	StdComputeLinearSolution (u, domainDisc, solver)
function util rates static	StdComputeNonLinearSolution (u, domainDisc, solver)
function util rates static	StdMaxLevelPadding (p)
function util rates static	StdMinLevelPadding (p)
function util rates static	StdPrepareInitialGuess (u, lev, minLev, maxLev, domainDisc, solver)
function util rates static StdLabel	XLatex (x)
function util rates static StdLabel	XPdf (x)
function util rates static StdLabel	YLatex (f, t, n)
function util rates static StdLabel	YPdf (f, t, n)

Function Documentation

compute()

function util rates static compute

(

ConvRateSetup

)

Computes convergence rates for a static problem

In the convergence rate setup the following parameters can be passed:

• (required) CreateDomain()
  function used to create Domain
• (required) CreateApproxSpace(dom, discType, p)
  function used to create ApproximationSpace
• (required) CreateDomainDisc(approxSpace, discType, p)
  function used to create Domain Discretization
• (required) CreateSolver(approxSpace, discType, p)
  function used to create Solver
• (required) DiscTypes
  Array containing types, orders and level to be looped
• (optional) ComputeSolution(u, domainDisc, solver)
  function used to compute solution
• (optional) PrepareInitialGuess
  function used to prepare Initial Guess
• (optional) ExactSol
  Array containing exact solution as a function
• (optional) ExactGrad
  Array containing exact gradients as a function

Parameters

ConvRate

Setup setup used

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :193-731

MeasLatexP()

function util rates static StdLabel MeasLatexP	(	disc	,
		p
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :110-112

function util.rates.static.StdLabel.MeasLatexP(disc, p)
  return disc.." $\\mathbb{P}_{"..p.."}$"
end

MeasLatexQ()

function util rates static StdLabel MeasLatexQ	(	disc	,
		p
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :114-116

function util.rates.static.StdLabel.MeasLatexQ(disc, p)
  return disc.." $\\mathbb{Q}_{"..p.."}$"
end

MeasPdfP()

function util rates static StdLabel MeasPdfP	(	disc	,
		p
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :137-139

function util.rates.static.StdLabel.MeasPdfP(disc, p)
  return disc.." $P_"..p.."$"
end

References p.

MeasPdfQ()

function util rates static StdLabel MeasPdfQ	(	disc	,
		p
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :141-143

function util.rates.static.StdLabel.MeasPdfQ(disc, p)
  return disc.." $Q_"..p.."$"
end

NoMaxLevelPadding()

function util rates static NoMaxLevelPadding

(

p

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :96-98

function util.rates.static.NoMaxLevelPadding(p)
  return 0
end

NoMinLevelPadding()

function util rates static NoMinLevelPadding

(

p

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :100-102

function util.rates.static.NoMinLevelPadding(p)
  return 0
end

replot()

function util rates static replot	(	gpOptions	,
		file
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :734-761

StdComputeLinearSolution()

function util rates static StdComputeLinearSolution	(	u	,
		domainDisc	,
		solver
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :53-76

StdComputeNonLinearSolution()

function util rates static StdComputeNonLinearSolution	(	u	,
		domainDisc	,
		solver
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :78-85

function util.rates.static.StdComputeNonLinearSolution(u, domainDisc, solver)
 
  solver:init(AssembledOperator(domainDisc, u:grid_level()))
  if solver:apply(u) == false then
     print (">> Newton solver apply failed."); exit();
  end
  write(">> Newton Solver done.\n")
end

StdMaxLevelPadding()

function util rates static StdMaxLevelPadding

(

p

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :87-89

function util.rates.static.StdMaxLevelPadding(p)
  return math.floor(p/2)
end

StdMinLevelPadding()

function util rates static StdMinLevelPadding

(

p

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :91-93

function util.rates.static.StdMinLevelPadding(p)
  return 0
end

StdPrepareInitialGuess()

function util rates static StdPrepareInitialGuess	(	u	,
		lev	,
		minLev	,
		maxLev	,
		domainDisc	,
		solver
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :41-50

function util.rates.static.StdPrepareInitialGuess(u, lev, minLev, maxLev,
 
  if lev > minLev then  
    Prolongate(u[lev], u[lev-1]);
    write(">> Solution interpolated as start value from coarser level.\n")
  else
    u[lev]:set(0.0)
    write(">> Solution set to zero on coarsest level.\n") 
  end   
end

XLatex()

function util rates static StdLabel XLatex

(

x

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :118-121

function util.rates.static.StdLabel.XLatex(x)
  local gpXLabel ={ DoFs = "Anzahl Unbekannte", h = "h (Gitterweite)"}
  return gpXLabel[x]
end

XPdf()

function util rates static StdLabel XPdf

(

x

)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :145-148

function util.rates.static.StdLabel.XPdf(x)
  local gpXLabel ={ DoFs = "Anzahl Unbekannte", h = "h (Gitterweite)"}
  return gpXLabel[x]
end

YLatex()

function util rates static StdLabel YLatex	(	f	,
		t	,
		n
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :123-135

function util.rates.static.StdLabel.YLatex(f, t, n)
  local gpType = {  ["l-exact"] =   "{}",   
            ["l-lmax"] =  "h_{\\text{min}}",
            ["l-prev"] =  "{h/2}",
          }
  local gpNorm =  { l2 = "L_2", h1 = "H^1"}
  
  if t == "interpol" then
    return "$\\norm{\\mathcal{I}_h("..f..") - "..f.."}_{"..gpNorm[n].."}$"
  else
    return "$\\norm{"..f.."_h - "..f.."_{"..gpType[t].."} }_{ "..gpNorm[n].."}$"
  end
end

YPdf()

function util rates static StdLabel YPdf	(	f	,
		t	,
		n
	)

location: /home/runner/work/docs/docs/ug4/ugcore/scripts/util / conv_rates_static.lua :150-162

function util.rates.static.StdLabel.YPdf(f, t, n)
  local gpType = {  ["l-exact"] =   "{}",   
            ["l-lmax"] =  "h_{\\text{min}}",
            ["l-prev"] =  "{h/2}",
          }
  local gpNorm =  { l2 = "L_2", h1 = "H^1"}
  
  if t == "interpol" then
    return "$|| I_h("..f..") - "..f.." ||_{"..gpNorm[n].."}$"
  else
    return "$|| "..f.."_h - "..f.."_{"..gpType[t].."} ||_{"..gpNorm[n].."}$"
  end
end