/*
 * Copyright (C)  NHR@FAU, University Erlangen-Nuremberg.
 * All rights reserved. This file is part of nusif-solver.
 * Use of this source code is governed by a MIT style
 * license that can be found in the LICENSE file.
 */
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "allocate.h"
#include "parameter.h"
#include "solver.h"
#include "util.h"

#define P(i, j)    p[(j) * (imax + 2) + (i)]
#define F(i, j)    f[(j) * (imax + 2) + (i)]
#define G(i, j)    g[(j) * (imax + 2) + (i)]
#define U(i, j)    u[(j) * (imax + 2) + (i)]
#define V(i, j)    v[(j) * (imax + 2) + (i)]
#define S(i, j)    s[(j) * (imax + 2) + (i)]
#define E(i, j)    e[(j) * (imax + 2) + (i)]
#define R(i, j)    r[(j) * (imax + 2) + (i)]
#define oldR(i, j) oldr[(j) * (imax + 2) + (i)]
#define oldE(i, j) olde[(j) * (imax + 2) + (i)]
#define RHS(i, j)  rhs[(j) * (imax + 2) + (i)]

static double distance(double i, double j, double iCenter, double jCenter)
{
    return sqrt(pow(iCenter - i, 2) + pow(jCenter - j, 2) * 1.0);
}

void print(Solver* solver, double* grid)
{
    int imax = solver->grid.imax;
    int jmax = solver->grid.jmax;

    for (int j = 0; j < jmax + 2; j++) {
        printf("%02d: ", j);
        for (int i = 0; i < imax + 2; i++) {
            printf("%3.2f  ", grid[j * (imax + 2) + i]);
        }
        printf("\n");
    }
    fflush(stdout);
}

void printGrid(Solver* solver, int* grid)
{
    int imax = solver->grid.imax;
    int jmax = solver->grid.jmax;

    for (int j = 0; j < jmax + 2; j++) {
        printf("%02d: ", j);
        for (int i = 0; i < imax + 2; i++) {
            printf("%2d  ", grid[j * (imax + 2) + i]);
        }
        printf("\n");
    }
    fflush(stdout);
}

static void printConfig(Solver* solver)
{
    printf("Parameters for #%s#\n", solver->problem);
    printf("Boundary conditions Left:%d Right:%d Bottom:%d Top:%d\n",
        solver->bcLeft,
        solver->bcRight,
        solver->bcBottom,
        solver->bcTop);
    printf("\tReynolds number: %.2f\n", solver->re);
    printf("\tGx Gy: %.2f %.2f\n", solver->gx, solver->gy);
    printf("Geometry data:\n");
    printf("\tDomain box size (x, y): %.2f, %.2f\n",
        solver->grid.xlength,
        solver->grid.ylength);
    printf("\tCells (x, y): %d, %d\n", solver->grid.imax, solver->grid.jmax);
    printf("Timestep parameters:\n");
    printf("\tDefault stepsize: %.2f, Final time %.2f\n", solver->dt, solver->te);
    printf("\tdt bound: %.6f\n", solver->dtBound);
    printf("\tTau factor: %.2f\n", solver->tau);
    printf("Iterative solver parameters:\n");
    printf("\tMax iterations: %d\n", solver->itermax);
    printf("\tepsilon (stopping tolerance) : %f\n", solver->eps);
    printf("\tgamma factor: %f\n", solver->gamma);
    printf("\tomega (SOR relaxation): %f\n", solver->omega);
}

void initSolver(Solver* solver, Parameter* params)
{
    solver->problem      = params->name;
    solver->bcLeft       = params->bcLeft;
    solver->bcRight      = params->bcRight;
    solver->bcBottom     = params->bcBottom;
    solver->bcTop        = params->bcTop;
    solver->grid.imax    = params->imax;
    solver->grid.jmax    = params->jmax;
    solver->grid.xlength = params->xlength;
    solver->grid.ylength = params->ylength;
    solver->grid.dx      = params->xlength / params->imax;
    solver->grid.dy      = params->ylength / params->jmax;
    solver->eps          = params->eps;
    solver->omega        = params->omg;
    solver->itermax      = params->itermax;
    solver->re           = params->re;
    solver->gx           = params->gx;
    solver->gy           = params->gy;
    solver->dt           = params->dt;
    solver->te           = params->te;
    solver->tau          = params->tau;
    solver->gamma        = params->gamma;
    solver->rho          = params->rho;
    solver->levels       = params->levels;
    solver->currentlevel = 0;

    int imax   = solver->grid.imax;
    int jmax   = solver->grid.jmax;
    int levels = solver->levels;

    size_t size_level = levels * (imax + 2) * (jmax + 2) * sizeof(double);

    size_t size = (imax + 2) * (jmax + 2) * sizeof(double);
    solver->u   = allocate(64, size);
    solver->v   = allocate(64, size);
    solver->s   = allocate(64, size);
    solver->p   = allocate(64, size);
    solver->rhs = allocate(64, size);
    solver->f   = allocate(64, size);
    solver->g   = allocate(64, size);

    solver->r = malloc(levels * sizeof(double*));
    solver->e = malloc(levels * sizeof(double*));

    for (int j = 0; j < levels; ++j) {

        solver->r[j] = allocate(64, size);
        solver->e[j] = allocate(64, size);
    }

    for (int i = 0; i < (imax + 2) * (jmax + 2); i++) {

        solver->u[i]   = params->u_init;
        solver->v[i]   = params->v_init;
        solver->p[i]   = params->p_init;
        solver->rhs[i] = 0.0;
        solver->f[i]   = 0.0;
        solver->g[i]   = 0.0;
        solver->s[i]   = NONE;
        for (int j = 0; j < levels; ++j) {

            solver->r[j][i] = 0.0;
            solver->e[j][i] = 0.0;
        }
    }

    double dx        = solver->grid.dx;
    double dy        = solver->grid.dy;
    double invSqrSum = 1.0 / (dx * dx) + 1.0 / (dy * dy);
    solver->dtBound  = 0.5 * solver->re * 1.0 / invSqrSum;

    double xCenter = 0, yCenter = 0, radius = 0;
    double x1 = 0, x2 = 0, y1 = 0, y2 = 0;

    int* s = solver->s;

    switch (params->shape) {
    case NOSHAPE:
        break;
    case RECT:
        x1 = params->xCenter - params->xRectLength / 2;
        x2 = params->xCenter + params->xRectLength / 2;
        y1 = params->yCenter - params->yRectLength / 2;
        y2 = params->yCenter + params->yRectLength / 2;

        for (int j = 1; j < jmax + 1; j++) {
            for (int i = 1; i < imax + 1; i++) {
                if ((x1 <= (i * dx)) && ((i * dx) <= x2) && (y1 <= (j * dy)) &&
                    ((j * dy) <= y2)) {
                    S(i, j) = LOCAL;
                }
            }
        }

        break;
    case CIRCLE:
        xCenter = params->xCenter;
        yCenter = params->yCenter;
        radius  = params->circleRadius;

        for (int j = 1; j < jmax + 1; j++) {
            for (int i = 1; i < imax + 1; i++) {
                if (distance((i * dx), (j * dy), xCenter, yCenter) <= radius) {
                    S(i, j) = LOCAL;
                }
            }
        }

        break;
    default:
        break;
    }

    if (params->shape != NOSHAPE) {
        for (int j = 1; j < jmax + 1; j++) {
            for (int i = 1; i < imax + 1; i++) {

                if (S(i, j - 1) == NONE && S(i, j + 1) == LOCAL && S(i, j) == LOCAL)
                    S(i, j) = BOTTOM; // TOP
                if (S(i - 1, j) == NONE && S(i + 1, j) == LOCAL && S(i, j) == LOCAL)
                    S(i, j) = LEFT; // LEFT
                if (S(i + 1, j) == NONE && S(i - 1, j) == LOCAL && S(i, j) == LOCAL)
                    S(i, j) = RIGHT; // RIGHT
                if (S(i, j + 1) == NONE && S(i, j - 1) == LOCAL && S(i, j) == LOCAL)
                    S(i, j) = TOP; // BOTTOM
                if (S(i - 1, j - 1) == NONE && S(i, j - 1) == NONE &&
                    S(i - 1, j) == NONE && S(i + 1, j + 1) == LOCAL &&
                    (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == BOTTOM))
                    S(i, j) = BOTTOMLEFT; // TOPLEFT
                if (S(i + 1, j - 1) == NONE && S(i, j - 1) == NONE &&
                    S(i + 1, j) == NONE && S(i - 1, j + 1) == LOCAL &&
                    (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == BOTTOM))
                    S(i, j) = BOTTOMRIGHT; // TOPRIGHT
                if (S(i - 1, j + 1) == NONE && S(i - 1, j) == NONE &&
                    S(i, j + 1) == NONE && S(i + 1, j - 1) == LOCAL &&
                    (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == TOP))
                    S(i, j) = TOPLEFT; // BOTTOMLEFT
                if (S(i + 1, j + 1) == NONE && S(i + 1, j) == NONE &&
                    S(i, j + 1) == NONE && S(i - 1, j - 1) == LOCAL &&
                    (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == TOP))
                    S(i, j) = TOPRIGHT; // BOTTOMRIGHT
            }
        }
    }

#ifdef VERBOSE
    printConfig(solver);
#endif
}

static double maxElement(Solver* solver, double* m)
{
    int size      = (solver->grid.imax + 2) * (solver->grid.jmax + 2);
    double maxval = DBL_MIN;

    for (int i = 0; i < size; i++) {
        maxval = MAX(maxval, fabs(m[i]));
    }

    return maxval;
}

void computeRHS(Solver* solver)
{
    int imax    = solver->grid.imax;
    int jmax    = solver->grid.jmax;
    double idx  = 1.0 / solver->grid.dx;
    double idy  = 1.0 / solver->grid.dy;
    double idt  = 1.0 / solver->dt;
    double* rhs = solver->rhs;
    double* f   = solver->f;
    double* g   = solver->g;
    int* s      = solver->s;

    for (int j = 1; j < jmax + 1; j++) {
        for (int i = 1; i < imax + 1; i++) {
            RHS(i, j) = idt *
                        ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy);
        }
    }
}

void normalizePressure(Solver* solver)
{
    int size    = (solver->grid.imax + 2) * (solver->grid.jmax + 2);
    double* p   = solver->p;
    double avgP = 0.0;

    for (int i = 0; i < size; i++) {
        avgP += p[i];
    }
    avgP /= size;

    for (int i = 0; i < size; i++) {
        p[i] = p[i] - avgP;
    }
}

void computeTimestep(Solver* solver)
{
    double dt   = solver->dtBound;
    double dx   = solver->grid.dx;
    double dy   = solver->grid.dy;
    double umax = maxElement(solver, solver->u);
    double vmax = maxElement(solver, solver->v);

    if (umax > 0) {
        dt = (dt > dx / umax) ? dx / umax : dt;
    }
    if (vmax > 0) {
        dt = (dt > dy / vmax) ? dy / vmax : dt;
    }

    solver->dt = dt * solver->tau;
}

void setBoundaryConditions(Solver* solver)
{
    int imax  = solver->grid.imax;
    int jmax  = solver->grid.jmax;
    double* u = solver->u;
    double* v = solver->v;

    // Left boundary
    switch (solver->bcLeft) {
    case NOSLIP:
        for (int j = 1; j < jmax + 1; j++) {
            U(0, j) = 0.0;
            V(0, j) = -V(1, j);
        }
        break;
    case SLIP:
        for (int j = 1; j < jmax + 1; j++) {
            U(0, j) = 0.0;
            V(0, j) = V(1, j);
        }
        break;
    case OUTFLOW:
        for (int j = 1; j < jmax + 1; j++) {
            U(0, j) = U(1, j);
            V(0, j) = V(1, j);
        }
        break;
    case PERIODIC:
        break;
    }

    // Right boundary
    switch (solver->bcRight) {
    case NOSLIP:
        for (int j = 1; j < jmax + 1; j++) {
            U(imax, j)     = 0.0;
            V(imax + 1, j) = -V(imax, j);
        }
        break;
    case SLIP:
        for (int j = 1; j < jmax + 1; j++) {
            U(imax, j)     = 0.0;
            V(imax + 1, j) = V(imax, j);
        }
        break;
    case OUTFLOW:
        for (int j = 1; j < jmax + 1; j++) {
            U(imax, j)     = U(imax - 1, j);
            V(imax + 1, j) = V(imax, j);
        }
        break;
    case PERIODIC:
        break;
    }

    // Bottom boundary
    switch (solver->bcBottom) {
    case NOSLIP:
        for (int i = 1; i < imax + 1; i++) {
            V(i, 0) = 0.0;
            U(i, 0) = -U(i, 1);
        }
        break;
    case SLIP:
        for (int i = 1; i < imax + 1; i++) {
            V(i, 0) = 0.0;
            U(i, 0) = U(i, 1);
        }
        break;
    case OUTFLOW:
        for (int i = 1; i < imax + 1; i++) {
            U(i, 0) = U(i, 1);
            V(i, 0) = V(i, 1);
        }
        break;
    case PERIODIC:
        break;
    }

    // Top boundary
    switch (solver->bcTop) {
    case NOSLIP:
        for (int i = 1; i < imax + 1; i++) {
            V(i, jmax)     = 0.0;
            U(i, jmax + 1) = -U(i, jmax);
        }
        break;
    case SLIP:
        for (int i = 1; i < imax + 1; i++) {
            V(i, jmax)     = 0.0;
            U(i, jmax + 1) = U(i, jmax);
        }
        break;
    case OUTFLOW:
        for (int i = 1; i < imax + 1; i++) {
            U(i, jmax + 1) = U(i, jmax);
            V(i, jmax)     = V(i, jmax - 1);
        }
        break;
    case PERIODIC:
        break;
    }
}

void setSpecialBoundaryCondition(Solver* solver)
{
    int imax   = solver->grid.imax;
    int jmax   = solver->grid.jmax;
    double mDy = solver->grid.dy;
    double* u  = solver->u;
    int* s     = solver->s;

    if (strcmp(solver->problem, "dcavity") == 0) {
        for (int i = 1; i < imax; i++) {
            U(i, jmax + 1) = 2.0 - U(i, jmax);
        }
    } else if (strcmp(solver->problem, "canal") == 0) {
        double ylength = solver->grid.ylength;
        double y;

        for (int j = 1; j < jmax + 1; j++) {
            y       = mDy * (j - 0.5);
            U(0, j) = y * (ylength - y) * 4.0 / (ylength * ylength);
        }
    } else if (strcmp(solver->problem, "backstep") == 0) {
        for (int j = 1; j < jmax + 1; j++) {
            if (S(0, j) == NONE) U(0, j) = 1.0;
        }
    } else if (strcmp(solver->problem, "karman") == 0) {
        for (int j = 1; j < jmax + 1; j++) {
            U(0, j) = 1.0;
        }
    }
}

void setObjectBoundaryCondition(Solver* solver)
{
    int imax  = solver->grid.imax;
    int jmax  = solver->grid.jmax;
    double* u = solver->u;
    double* v = solver->v;
    int* s    = solver->s;

    for (int j = 1; j < jmax + 1; j++) {
        for (int i = 1; i < imax + 1; i++) {
            switch (S(i, j)) {
            case TOP:
                U(i, j)     = -U(i, j + 1);
                U(i - 1, j) = -U(i - 1, j + 1);
                V(i, j)     = 0.0;
                break;
            case BOTTOM:
                U(i, j)     = -U(i, j - 1);
                U(i - 1, j) = -U(i - 1, j - 1);
                V(i, j)     = 0.0;
                break;
            case LEFT:
                U(i - 1, j) = 0.0;
                V(i, j)     = -V(i - 1, j);
                V(i, j - 1) = -V(i - 1, j - 1);
                break;
            case RIGHT:
                U(i, j)     = 0.0;
                V(i, j)     = -V(i + 1, j);
                V(i, j - 1) = -V(i + 1, j - 1);
                break;
            case TOPLEFT:
                U(i, j)     = -U(i, j + 1);
                U(i - 1, j) = 0.0;
                V(i, j)     = 0.0;
                V(i, j - 1) = -V(i - 1, j - 1);
                break;
            case TOPRIGHT:
                U(i, j)     = 0.0;
                U(i - 1, j) = -U(i - 1, j + 1);
                V(i, j)     = 0.0;
                V(i, j - 1) = -V(i + 1, j - 1);
                break;
            case BOTTOMLEFT:
                U(i, j)     = -U(i, j - 1);
                U(i - 1, j) = 0.0;
                V(i, j)     = -V(i - 1, j);
                V(i, j - 1) = 0.0;
                break;
            case BOTTOMRIGHT:
                U(i, j)     = 0.0;
                U(i - 1, j) = -U(i - 1, j - 1);
                V(i, j)     = -V(i, j + 1);
                V(i, j - 1) = 0.0;
                break;
            }
        }
    }
}

void computeFG(Solver* solver)
{
    double* u        = solver->u;
    double* v        = solver->v;
    double* f        = solver->f;
    double* g        = solver->g;
    int* s           = solver->s;
    int imax         = solver->grid.imax;
    int jmax         = solver->grid.jmax;
    double gx        = solver->gx;
    double gy        = solver->gy;
    double gamma     = solver->gamma;
    double dt        = solver->dt;
    double inverseRe = 1.0 / solver->re;
    double inverseDx = 1.0 / solver->grid.dx;
    double inverseDy = 1.0 / solver->grid.dy;
    double du2dx, dv2dy, duvdx, duvdy;
    double du2dx2, du2dy2, dv2dx2, dv2dy2;

    for (int j = 1; j < jmax + 1; j++) {
        for (int i = 1; i < imax + 1; i++) {
            if (S(i, j) == NONE) {
                du2dx = inverseDx * 0.25 *
                            ((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
                                (U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
                        gamma * inverseDx * 0.25 *
                            (fabs(U(i, j) + U(i + 1, j)) * (U(i, j) - U(i + 1, j)) +
                                fabs(U(i, j) + U(i - 1, j)) * (U(i, j) - U(i - 1, j)));

                duvdy = inverseDy * 0.25 *
                            ((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
                                (V(i, j - 1) + V(i + 1, j - 1)) *
                                    (U(i, j) + U(i, j - 1))) +
                        gamma * inverseDy * 0.25 *
                            (fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
                                fabs(V(i, j - 1) + V(i + 1, j - 1)) *
                                    (U(i, j) - U(i, j - 1)));

                du2dx2 = inverseDx * inverseDx *
                         (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
                du2dy2 = inverseDy * inverseDy *
                         (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
                F(i, j) = U(i, j) +
                          dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);

                duvdx = inverseDx * 0.25 *
                            ((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
                                (U(i - 1, j) + U(i - 1, j + 1)) *
                                    (V(i, j) + V(i - 1, j))) +
                        gamma * inverseDx * 0.25 *
                            (fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
                                fabs(U(i - 1, j) + U(i - 1, j + 1)) *
                                    (V(i, j) - V(i - 1, j)));

                dv2dy = inverseDy * 0.25 *
                            ((V(i, j) + V(i, j + 1)) * (V(i, j) + V(i, j + 1)) -
                                (V(i, j) + V(i, j - 1)) * (V(i, j) + V(i, j - 1))) +
                        gamma * inverseDy * 0.25 *
                            (fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
                                fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));

                dv2dx2 = inverseDx * inverseDx *
                         (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
                dv2dy2 = inverseDy * inverseDy *
                         (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
                G(i, j) = V(i, j) +
                          dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
            } else {
                switch (S(i, j)) {
                case TOP:
                    G(i, j) = V(i, j);
                    break;
                case BOTTOM:
                    G(i, j - 1) = V(i, j - 1);
                    break;
                case LEFT:
                    F(i - 1, j) = U(i - 1, j);
                    break;
                case RIGHT:
                    F(i, j) = U(i, j);
                    break;
                case TOPLEFT:
                    F(i - 1, j) = U(i - 1, j);
                    G(i, j)     = V(i, j);
                    break;
                case TOPRIGHT:
                    F(i, j) = U(i, j);
                    G(i, j) = V(i, j);
                    break;
                case BOTTOMLEFT:
                    F(i - 1, j) = U(i - 1, j);
                    G(i, j - 1) = V(i, j - 1);
                    break;
                case BOTTOMRIGHT:
                    F(i, j)     = U(i, j);
                    G(i, j - 1) = V(i, j - 1);
                    break;
                }
            }
        }
    }

    /* ---------------------- boundary of F --------------------------- */
    for (int j = 1; j < jmax + 1; j++) {
        F(0, j)    = U(0, j);
        F(imax, j) = U(imax, j);
    }

    /* ---------------------- boundary of G --------------------------- */
    for (int i = 1; i < imax + 1; i++) {
        G(i, 0)    = V(i, 0);
        G(i, jmax) = V(i, jmax);
    }
}

void adaptUV(Solver* solver)
{
    int imax       = solver->grid.imax;
    int jmax       = solver->grid.jmax;
    double* p      = solver->p;
    double* u      = solver->u;
    double* v      = solver->v;
    int* s         = solver->s;
    double* f      = solver->f;
    double* g      = solver->g;
    double factorX = solver->dt / solver->grid.dx;
    double factorY = solver->dt / solver->grid.dy;

    double val = 0;

    for (int j = 1; j < jmax + 1; j++) {
        for (int i = 1; i < imax + 1; i++) {
            U(i, j) = F(i, j) - (P(i + 1, j) - P(i, j)) * factorX;
            V(i, j) = G(i, j) - (P(i, j + 1) - P(i, j)) * factorY;
        }
    }
}

double smoothRB(Solver* solver)
{
    int imax      = solver->grid.imax;
    int jmax      = solver->grid.jmax;
    double eps    = solver->eps;
    int itermax   = solver->itermax;
    double dx2    = solver->grid.dx * solver->grid.dx;
    double dy2    = solver->grid.dy * solver->grid.dy;
    double idx2   = 1.0 / dx2;
    double idy2   = 1.0 / dy2;
    double factor = solver->omega * 0.5 * (dx2 * dy2) / (dx2 + dy2);
    double* p     = solver->p;
    double* r     = solver->r[solver->currentlevel];
    double* rhs   = solver->rhs;
    double epssq  = eps * eps;
    int it        = 0;
    double res    = 1.0;
    int pass, jsw, isw;

    jsw = 1;

    for (pass = 0; pass < 2; pass++) {
        isw = jsw;

        for (int j = 1; j < jmax + 1; j++) {
            for (int i = isw; i < imax + 1; i += 2) {

                R(i, j) = RHS(i, j) -
                          ((P(i + 1, j) - 2.0 * P(i, j) + P(i - 1, j)) * idx2 +
                              (P(i, j + 1) - 2.0 * P(i, j) + P(i, j - 1)) * idy2);

                P(i, j) -= (factor * R(i, j));
                res += (R(i, j) * R(i, j));
            }
            isw = 3 - isw;
        }
        jsw = 3 - jsw;
    }

    res = res / (double)(imax * jmax);
    return res;
}

void multiGrid(Solver* solver)
{
    double res = 0.0;
    int imax   = solver->grid.imax;
    int jmax   = solver->grid.jmax;
    if (solver->currentlevel == (solver->levels - 1)) {
        for (int i = 0; i < 5; i++) {
            smoothRB(solver);
        }
        return;
    }

    for (int i = 0; i < 5; i++) {
        smoothRB(solver);
        if (solver->currentlevel == 0) {

            double* p = solver->p;

            for (int i = 1; i < imax + 1; i++) {
                P(i, 0)        = P(i, 1);
                P(i, jmax + 1) = P(i, jmax);
            }

            for (int j = 1; j < jmax + 1; j++) {
                P(0, j)        = P(1, j);
                P(imax + 1, j) = P(imax, j);
            }
        }
    }
    Solver coarseSolver = copySolver(solver);

    // restrict
    restrictMG(solver);

    coarseSolver.p   = solver->e[coarseSolver.currentlevel];
    coarseSolver.rhs = solver->r[coarseSolver.currentlevel];
    coarseSolver.grid.imax /= 2;
    coarseSolver.grid.jmax /= 2;

    // MGSolver on residual and error.
    multiGrid(&coarseSolver);

    // prolongate
    prolongate(solver);

    // correct p on finest level using residual
    correct(solver);

    if (solver->currentlevel == 0) {

        double* p = solver->p;

        for (int i = 1; i < imax + 1; i++) {
            P(i, 0)        = P(i, 1);
            P(i, jmax + 1) = P(i, jmax);
        }

        for (int j = 1; j < jmax + 1; j++) {
            P(0, j)        = P(1, j);
            P(imax + 1, j) = P(imax, j);
        }
    }

    for (int i = 0; i < 5; i++) {
        res = smoothRB(solver);
        if (solver->currentlevel == 0) {

            double* p = solver->p;

            for (int i = 1; i < imax + 1; i++) {
                P(i, 0)        = P(i, 1);
                P(i, jmax + 1) = P(i, jmax);
            }

            for (int j = 1; j < jmax + 1; j++) {
                P(0, j)        = P(1, j);
                P(imax + 1, j) = P(imax, j);
            }
        }
    }
#ifdef VERBOSE
    if (solver->currentlevel == 0) {
        printf("Residuum: %.6f\n", res);
    }
#endif
}

void restrictMG(Solver* solver)
{
    int imax     = solver->grid.imax;
    int jmax     = solver->grid.jmax;
    double* r    = solver->r[solver->currentlevel + 1];
    double* oldr = solver->r[solver->currentlevel];

    for (int j = 1; j < jmax + 1; j++) {
        for (int i = 1; i < imax + 1; ++i) {
            R(i, j) = (oldR(2 * i - 1, 2 * j - 1) + oldR(2 * i, 2 * j - 1) * 2 +
                          oldR(2 * i + 1, 2 * j - 1) + oldR(2 * i - 1, 2 * j) * 2 +
                          oldR(2 * i, 2 * j) * 4 + oldR(2 * i + 1, 2 * j) * 2 +
                          oldR(2 * i - 1, 2 * j + 1) + oldR(2 * i, 2 * j + 1) * 2 +
                          oldR(2 * i + 1, 2 * j + 1)) /
                      16.0;
        }
    }
}

void prolongate(Solver* solver)
{
    int imax     = solver->grid.imax;
    int jmax     = solver->grid.jmax;
    double* olde = solver->r[solver->currentlevel + 1];
    double* e    = solver->r[solver->currentlevel];

    for (int j = 2; j < jmax + 1; j += 2) {
        for (int i = 2; i < imax + 1; i += 2) {
            E(i, j) = oldE(i / 2, j / 2);
        }
    }
}

void correct(Solver* solver)
{
    int imax  = solver->grid.imax;
    int jmax  = solver->grid.jmax;
    double* p = solver->p;
    double* e = solver->e[solver->currentlevel];
    for (int j = 1; j < jmax + 1; ++j) {
        for (int i = 1; i < imax + 1; ++i) {
            P(i, j) += E(i, j);
        }
    }
}

Solver copySolver(Solver* solver)
{
    Solver newSolver;
    newSolver.problem      = solver->problem;
    newSolver.bcLeft       = solver->bcLeft;
    newSolver.bcRight      = solver->bcRight;
    newSolver.bcBottom     = solver->bcBottom;
    newSolver.bcTop        = solver->bcTop;
    newSolver.grid.imax    = solver->grid.imax;
    newSolver.grid.jmax    = solver->grid.jmax;
    newSolver.grid.xlength = solver->grid.xlength;
    newSolver.grid.ylength = solver->grid.ylength;
    newSolver.grid.dx      = solver->grid.xlength / solver->grid.imax;
    newSolver.grid.dy      = solver->grid.ylength / solver->grid.jmax;
    newSolver.eps          = solver->eps;
    newSolver.omega        = solver->omega;
    newSolver.itermax      = solver->itermax;
    newSolver.re           = solver->re;
    newSolver.gx           = solver->gx;
    newSolver.gy           = solver->gy;
    newSolver.dt           = solver->dt;
    newSolver.te           = solver->te;
    newSolver.tau          = solver->tau;
    newSolver.gamma        = solver->gamma;
    newSolver.rho          = solver->rho;
    newSolver.levels       = solver->levels;
    newSolver.currentlevel = solver->currentlevel + 1;

    newSolver.r = solver->r;
    newSolver.e = solver->e;

    return newSolver;
}

void writeResult(Solver* solver)
{
    int imax  = solver->grid.imax;
    int jmax  = solver->grid.jmax;
    double dx = solver->grid.dx;
    double dy = solver->grid.dy;
    double* p = solver->p;
    double* u = solver->u;
    double* v = solver->v;
    double x = 0.0, y = 0.0;

    FILE* fp;
    fp = fopen("pressure.dat", "w");

    if (fp == NULL) {
        printf("Error!\n");
        exit(EXIT_FAILURE);
    }

    for (int j = 1; j < jmax + 1; j++) {
        y = (double)(j - 0.5) * dy;
        for (int i = 1; i < imax + 1; i++) {
            x = (double)(i - 0.5) * dx;
            fprintf(fp, "%.2f %.2f %f\n", x, y, P(i, j));
        }
        fprintf(fp, "\n");
    }

    fclose(fp);

    fp = fopen("velocity.dat", "w");

    if (fp == NULL) {
        printf("Error!\n");
        exit(EXIT_FAILURE);
    }

    for (int j = 1; j < jmax + 1; j++) {
        y = dy * (j - 0.5);
        for (int i = 1; i < imax + 1; i++) {
            x            = dx * (i - 0.5);
            double vel_u = (U(i, j) + U(i - 1, j)) / 2.0;
            double vel_v = (V(i, j) + V(i, j - 1)) / 2.0;
            double len   = sqrt((vel_u * vel_u) + (vel_v * vel_v));
            fprintf(fp, "%.2f %.2f %f %f %f\n", x, y, vel_u, vel_v, len);
        }
    }

    fclose(fp);
}