olekravchenko

Clear[n, e, Ne, Ef, lines, ns, es]
L = 6; nx = 201; dx = L/(nx - 1);
xTbl = Range[0, L, dx]; tEnd = 10;
Ne[t_] = Subscript[n, #][t] & /@ Range[1, nx];
Ef[t_] = Subscript[e, #][t] & /@ Range[1, nx];
eTbl = {Subscript[e, 1][t] == 10^-4, 
   Table[\[Kappa] D[Subscript[e, i][t], 
        t] + {1, -1}.{Subscript[e, i][t], 
         Subscript[e, i - 1][t]}/(h) == 1 - Subscript[n, i][t], {i, 2,
      nx - 1}], Subscript[e, nx][t] == Subscript[e, nx - 1][t]};

olekravchenko

%% Set Variables
qm =    circshift(qo,+ind);
pm =    circshift(po,+ind);
qp =    circshift(qo,-ind);
pp =    circshift(po,-ind);

%% Step 1: Reconstruction of flux \hat{f}_{i+1/2} value
% Reconstruction Polynomials
up0 = [-7 13 -4*h] * [qm; qo; pm] / 6;
up1 = [-1  5  2  ] * [qm; qo; qp] / 6;

olekravchenko

% --------
% RESIDUAL
% --------
% Along x
[axp,axm]=fluxsplitting_scalar(ax,'LF');
axm = circshift(axm,[0 1]);

[dqL,dpL] = HWENO5_reconstruction(axm,dx,q,p,[0 -1]);
[dqR,dpR] = HWENO5_reconstruction(axp,dx,q,p,[0 +1]);
dq = dqL + dqR;

olekravchenko

    program gdns2s_strat_new
    use omp_lib
    parameter (ni=998)
    parameter (nj=1250)
    !implicit double precision (a-h,o-z)

    real (kind=8), allocatable, dimension(:)    ::  x, y, ylt, roaxe, paxe
    real (kind=8), allocatable, dimension(:,:)  ::  ro, u, v, es, rox, ux, vx, esx, roy, uy, vy, esy, dksi

olekravchenko

upFt[t_, n_] := Product[Sinc[t 2^-k], {k, 1, n}]

Plot[{Sinc[2 \[Pi] t], upFt[2 \[Pi] t, 1], upFt[2 \[Pi] t, 2], 
  Cos[2 \[Pi] t]}, {t, -3.05, 3.05}, PlotRange -> All, 
 PlotStyle -> Thick,
 PlotLegends -> {"sinc(2\[Pi]t)", "sinc(\[Pi]t)", 
   "sinc(\[Pi]t)sinc(\[Pi]t/2)", "cos(x)"},
 ImageSize -> Large]

olekravchenko

from sympy import *
#from sympy import Symbol, solve
from sympy.solvers.solveset import linsolve

# Set symbolic parameters
x, a, b, c, d, h, ui, ui1, gi, gi1 = symbols('x, a, b, c, d, h, ui, ui1, gi, gi1')
# Set interpolation polynomials
f = a + b*x + c*x**2 + d*x**3
df = f.diff(x)
# Set constrains

olekravchenko

B3[x_] := BSplineBasis[3, 0.25 (x + 2)]
FTfupn[x_, n_, elemProd_] := 
 Sinc[x/2]^(n + 1) Product[Sinc[x 2^-i], {i, 2, elemProd}]
fupn[x_, n_, elemProd_, elemSum_] := 
 If[-((n + 2)/2) <= x && x <= (n + 2)/2, 
  2/(n + 2) (0.5 + 
     Sum[FTfupn[ (2 k \[Pi])/(n + 2), n, 
        elemProd] Cos[(2 k \[Pi])/(n + 2) x], {k, 1, elemSum}]), 0]

Plot[{B3[x], fupn[x, 2, 4, 15]}, {x, -2, 2}, 

olekravchenko

f[x_] := 1/2 - (4/\[Pi]) Arg[QPochhammer[I (2 x - 1)]]
upFT[t_] := Product[Sinc[t 2^-k], {k, 1, 5}]
up[x_] := 1/2 + Sum[Cos[\[Pi] k x] upFT[\[Pi] k], {k, 1, 25}]

Column@{
  Plot[{up[x - 1], f[x]}, {x, 0, 1}, PlotStyle -> Thick, 
   ImageSize -> 450],
  Plot[Abs@{up[x - 1] - f[x]}, {x, 0, 1}, PlotStyle -> Thick, 
   ImageSize -> 450]
  }

olekravchenko

(*
Author: Oleg Kravchenko;
Date: 18/6/16;
*)

ClearAll["Global`*"]
(*eup(x) function via convolution*)

eUP[k_, x_] := 2^k UnitBox[2^k x] Exp[x]
c1eUP[x_] := Convolve[eUP[0, s], eUP[1, s], s, x] // Evaluate

olekravchenko

(*Exponential atomic function*)

(*Fourier Transform*)
Sinch[x_] := If[x == 0, 0, Sinh[x]/x];
FTeup[a_, t_] := 
 Product[(Sinch[Log[a]/2])^-1 Sinch[Log[a]/2 - I t /2^j], {j, 1, 4}];
 
 (*Eup AF via Fourier Series*)
 eup[a_, x_] := 
 If[-1 <= x <= 1,