From b84aa107de51bc7c401871be0623652e260df23c Mon Sep 17 00:00:00 2001 From: afonsofrancof Date: Sun, 26 Nov 2023 15:17:10 +0000 Subject: [PATCH] OpenMP done --- Makefile | 6 +- relatorio.pdf | Bin 0 -> 371530 bytes src/MD2.cpp | 837 ++++++++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 840 insertions(+), 3 deletions(-) create mode 100644 relatorio.pdf create mode 100644 src/MD2.cpp diff --git a/Makefile b/Makefile index 2fc2a85..d202571 100644 --- a/Makefile +++ b/Makefile @@ -1,11 +1,11 @@ CC = gcc SRC = src/ -CFLAGS = # none +CFLAGS = -march=native -mtune=native -mavx -O2 -ftree-vectorize -fopenmp .DEFAULT_GOAL = MD.exe -MD.exe: $(SRC)/MD.cpp - $(CC) $(CFLAGS) $(SRC)MD.cpp -lm -march=native -mtune=native -mavx -O2 -ftree-vectorize -funroll-loops -o MD.exe +MD.exe: $(SRC)/MD2.cpp + $(CC) $(CFLAGS) $(SRC)MD2.cpp -lm -o MD.exe clean: rm ./MD.exe diff --git a/relatorio.pdf b/relatorio.pdf new file mode 100644 index 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Foley IV, Chelsea Sweet, Oyewumi Akinfenwa + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + + Electronic Contact: foleyj10@wpunj.edu + Mail Contact: Prof. Jonathan Foley + Department of Chemistry, William Paterson University + 300 Pompton Road + Wayne NJ 07470 + +*/ + +#include +#include +#include +#include +#include +#include + +// Readability + +typedef __m256d fourD; +typedef __m128d twoD; + +#define load_4d(ptr) _mm256_load_pd(ptr) +#define store_4d(ptr, val) _mm256_store_pd(ptr, val) +#define store_lower_1d(ptr, val) _mm_store_pd(ptr, val) +#define add_4d(a, b) _mm256_add_pd(a, b) +#define add_2d(a, b) _mm_add_pd(a, b) +#define hadd_4d(a, b) _mm256_hadd_pd(a, b) +#define sub_4d(a, b) _mm256_sub_pd(a, b) +#define mul_4d(a, b) _mm256_mul_pd(a, b) +#define div_4d(a, b) _mm256_div_pd(a, b) +#define create_4d(a) _mm256_set1_pd(a) +#define get_lower_2d(a) _mm256_castpd256_pd128(a) +#define get_upper_2d(a) _mm256_extractf128_pd(a, 1) + +#define ALIGNMENT 32 +// Number of particles +int N; + +// Lennard-Jones parameters in natural units! +double sigma = 1.; +double epsilon = 1.; +double m = 1.; +double kB = 1.; +double epsilon_8 = epsilon * 8.; + +double NA = 6.022140857e23; +double kBSI = 1.38064852e-23; // m^2*kg/(s^2*K) + +// Size of box, which will be specified in natural units +double L; + +// Initial Temperature in Natural Units +double Tinit; // 2; +// Vectors! +// +const int MAXPART = 5001; +// Position +double r[MAXPART][3]; +// Velocity +double v[MAXPART][3]; +// Acceleration +double a[MAXPART][3]; +// Force +double F[MAXPART][3]; + +// atom type +char atype[10]; +// Function prototypes +// initialize positions on simple cubic lattice, also calls function to +// initialize velocities +void initialize(); +// update positions and velocities using Velocity Verlet algorithm +// print particle coordinates to file for rendering via VMD or other animation +// software return 'instantaneous pressure' +double VelocityVerlet(double dt, int iter, double *PE, FILE *fp); +// Compute Force using F = -dV/dr +// solve F = ma for use in Velocity Verlet +void computeAccelerations(); +// Numerical Recipes function for generation gaussian distribution +double gaussdist(); +// Initialize velocities according to user-supplied initial Temperature +// (Tinit) +void initializeVelocities(); +// Compute total potential energy from particle coordinates +double Potential(); +// Compute mean squared velocity from particle velocities +double MeanSquaredVelocity(); +// Compute total kinetic energy from particle mass and velocities +double Kinetic(); + +int main() { + + // variable delcarations + int i; + double dt, Vol, Temp, Press, Pavg, Tavg, rho; + double VolFac, TempFac, PressFac, timefac; + double KE, PE, mvs, gc, Z; + char trash[10000], prefix[1000], tfn[1000], ofn[1000], afn[1000]; + FILE *infp, *tfp, *ofp, *afp; + + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf(" WELCOME TO WILLY P CHEM MD!\n"); + printf(" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf("\n ENTER A TITLE FOR YOUR CALCULATION!\n"); + scanf("%s", prefix); + strcpy(tfn, prefix); + strcat(tfn, "_traj.xyz"); + strcpy(ofn, prefix); + strcat(ofn, "_output.txt"); + strcpy(afn, prefix); + strcat(afn, "_average.txt"); + + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf(" TITLE ENTERED AS '%s'\n", prefix); + printf(" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + + /* Table of values for Argon relating natural units to SI units: + * These are derived from Lennard-Jones parameters from the article + * "Liquid argon: Monte carlo and molecular dynamics calculations" + * J.A. Barker , R.A. Fisher & R.O. Watts + * Mol. Phys., Vol. 21, 657-673 (1971) + * + * mass: 6.633e-26 kg = one natural unit of mass for + *argon, by definition energy: 1.96183e-21 J = one natural unit of + *energy for argon, directly from L-J parameters length: 3.3605e-10 m = + *one natural unit of length for argon, directly from L-J parameters + * volume: 3.79499-29 m^3 = one natural unit of volume for + *argon, by length^3 time: 1.951e-12 s = one natural unit of + *time for argon, by length*sqrt(mass/energy) + ***************************************************************************************/ + + // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + // Edit these factors to be computed in terms of basic properties in + // natural units of the gas being simulated + + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf(" WHICH NOBLE GAS WOULD YOU LIKE TO SIMULATE? (DEFAULT IS ARGON)\n"); + printf("\n FOR HELIUM, TYPE 'He' THEN PRESS 'return' TO CONTINUE\n"); + printf(" FOR NEON, TYPE 'Ne' THEN PRESS 'return' TO CONTINUE\n"); + printf(" FOR ARGON, TYPE 'Ar' THEN PRESS 'return' TO CONTINUE\n"); + printf(" FOR KRYPTON, TYPE 'Kr' THEN PRESS 'return' TO CONTINUE\n"); + printf(" FOR XENON, TYPE 'Xe' THEN PRESS 'return' TO CONTINUE\n"); + printf(" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + scanf("%s", atype); + + if (strcmp(atype, "He") == 0) { + + VolFac = 1.8399744000000005e-29; + PressFac = 8152287.336171632; + TempFac = 10.864459551225972; + timefac = 1.7572698825166272e-12; + } else if (strcmp(atype, "Ne") == 0) { + + VolFac = 2.0570823999999997e-29; + PressFac = 27223022.27659913; + TempFac = 40.560648991243625; + timefac = 2.1192341945685407e-12; + } else if (strcmp(atype, "Ar") == 0) { + + VolFac = 3.7949992920124995e-29; + PressFac = 51695201.06691862; + TempFac = 142.0950000000000; + timefac = 2.09618e-12; + // strcpy(atype,"Ar"); + } else if (strcmp(atype, "Kr") == 0) { + + VolFac = 4.5882712000000004e-29; + PressFac = 59935428.40275003; + TempFac = 199.1817584391428; + timefac = 8.051563913585078e-13; + } else if (strcmp(atype, "Xe") == 0) { + + VolFac = 5.4872e-29; + PressFac = 70527773.72794868; + TempFac = 280.30305642163006; + timefac = 9.018957925790732e-13; + } else { + + VolFac = 3.7949992920124995e-29; + PressFac = 51695201.06691862; + TempFac = 142.0950000000000; + timefac = 2.09618e-12; + strcpy(atype, "Ar"); + } + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf("\n YOU ARE SIMULATING %s GAS! \n", atype); + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + + printf("\n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf("\n YOU WILL NOW ENTER A FEW SIMULATION PARAMETERS\n"); + printf(" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); + printf("\n\n ENTER THE INTIAL TEMPERATURE OF YOUR GAS IN KELVIN\n"); + scanf("%lf", &Tinit); + // Make sure temperature is a positive number! + if (Tinit < 0.) { + printf("\n !!!!! ABSOLUTE TEMPERATURE MUST BE A POSITIVE " + "NUMBER! PLEASE " + "TRY AGAIN WITH A POSITIVE TEMPERATURE!!!\n"); + exit(0); + } + // Convert initial temperature from kelvin to natural units + Tinit /= TempFac; + + printf("\n\n ENTER THE NUMBER DENSITY IN moles/m^3\n"); + printf(" FOR REFERENCE, NUMBER DENSITY OF AN IDEAL GAS AT STP IS ABOUT 40 " + "moles/m^3\n"); + printf(" NUMBER DENSITY OF LIQUID ARGON AT 1 ATM AND 87 K IS ABOUT 35000 " + "moles/m^3\n"); + + scanf("%lf", &rho); + + N = 10 * 500; + Vol = N / (rho * NA); + + Vol /= VolFac; + + // Limiting N to MAXPART for practical reasons + if (N >= MAXPART) { + + printf("\n\n\n MAXIMUM NUMBER OF PARTICLES IS %i\n\n PLEASE " + "ADJUST YOUR " + "INPUT FILE ACCORDINGLY \n\n", + MAXPART); + exit(0); + } + // Check to see if the volume makes sense - is it too small? + // Remember VDW radius of the particles is 1 natural unit of length + // and volume = L*L*L, so if V = N*L*L*L = N, then all the particles + // will be initialized with an interparticle separation equal to 2xVDW + // radius + if (Vol < N) { + + printf("\n\n\n YOUR DENSITY IS VERY HIGH!\n\n"); + printf(" THE NUMBER OF PARTICLES IS %i AND THE AVAILABLE VOLUME " + "IS %f " + "NATURAL UNITS\n", + N, Vol); + printf(" SIMULATIONS WITH DENSITY GREATER THAN 1 PARTCICLE/(1 " + "Natural " + "Unit of Volume) MAY DIVERGE\n"); + printf(" PLEASE ADJUST YOUR INPUT FILE ACCORDINGLY AND RETRY\n\n"); + exit(0); + } + // Vol = L*L*L; + // Length of the box in natural units: + L = pow(Vol, (1. / 3)); + + // Files that we can write different quantities to + tfp = fopen(tfn, "w"); // The MD trajectory, coordinates of every + // particle at each timestep + ofp = fopen(ofn, + "w"); // Output of other quantities (T, P, gc, etc) at every timestep + afp = fopen(afn, "w"); // Average T, P, gc, etc from the simulation + + int NumTime; + if (strcmp(atype, "He") == 0) { + + // dt in natural units of time s.t. in SI it is 5 f.s. for all + // other gasses + dt = 0.2e-14 / timefac; + // We will run the simulation for NumTime timesteps. + // The total time will be NumTime*dt in natural units + // And NumTime*dt multiplied by the appropriate conversion factor + // for time in seconds + NumTime = 50000; + } else { + dt = 0.5e-14 / timefac; + NumTime = 200; + } + + // Put all the atoms in simple crystal lattice and give them random + // velocities that corresponds to the initial temperature we have + // specified + initialize(); + + // Based on their positions, calculate the ininial intermolecular forces + // The accellerations of each particle will be defined from the forces and + // their mass, and this will allow us to update their positions via + // Newton's law + computeAccelerations(); + + // Print number of particles to the trajectory file + fprintf(tfp, "%i\n", N); + + // We want to calculate the average Temperature and Pressure for the + // simulation The variables need to be set to zero initially + Pavg = 0; + Tavg = 0; + + int tenp = floor(NumTime / 10); + fprintf(ofp, " time (s) T(t) (K) P(t) (Pa) " + "Kinetic En. (n.u.) Potential En. (n.u.) Total En. (n.u.)\n"); + printf(" PERCENTAGE OF CALCULATION COMPLETE:\n ["); + for (i = 0; i < NumTime + 1; i++) { + + // This just prints updates on progress of the calculation for the + // users convenience + if (i == tenp) + printf(" 10 |"); + else if (i == 2 * tenp) + printf(" 20 |"); + else if (i == 3 * tenp) + printf(" 30 |"); + else if (i == 4 * tenp) + printf(" 40 |"); + else if (i == 5 * tenp) + printf(" 50 |"); + else if (i == 6 * tenp) + printf(" 60 |"); + else if (i == 7 * tenp) + printf(" 70 |"); + else if (i == 8 * tenp) + printf(" 80 |"); + else if (i == 9 * tenp) + printf(" 90 |"); + else if (i == 10 * tenp) + printf(" 100 ]\n"); + fflush(stdout); + + // This updates the positions and velocities using Newton's Laws + // Also computes the Pressure as the sum of momentum changes from + // wall collisions / timestep which is a Kinetic Theory of gasses + // concept of Pressure + Press = VelocityVerlet(dt, i + 1, &PE, tfp); + Press *= PressFac; + + // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + // Now we would like to calculate somethings about the system: + // Instantaneous mean velocity squared, Temperature, Pressure + // Potential, and Kinetic Energy + // We would also like to use the IGL to try to see if we can + // extract the gas constant + mvs = MeanSquaredVelocity(); + KE = Kinetic(); + + // Temperature from Kinetic Theory + Temp = m * mvs / (3 * kB) * TempFac; + + // Instantaneous gas constant and compressibility - not well + // defined because pressure may be zero in some instances because + // there will be zero wall collisions, pressure may be very high in + // some instances because there will be a number of collisions + gc = NA * Press * (Vol * VolFac) / (N * Temp); + Z = Press * (Vol * VolFac) / (N * kBSI * Temp); + + Tavg += Temp; + Pavg += Press; + + fprintf(ofp, " %8.4e %20.12f %20.12f %20.12f %20.12f %20.12f \n", i * dt * timefac, + Temp, Press, KE, PE, KE + PE); + } + + // Because we have calculated the instantaneous temperature and pressure, + // we can take the average over the whole simulation here + Pavg /= NumTime; + Tavg /= NumTime; + Z = Pavg * (Vol * VolFac) / (N * kBSI * Tavg); + gc = NA * Pavg * (Vol * VolFac) / (N * Tavg); + fprintf(afp, " Total Time (s) T (K) P (Pa) PV/nT " + "(J/(mol K)) Z V (m^3) N\n"); + fprintf(afp, " -------------- ----------- --------------- " + "-------------- --------------- ------------ -----------\n"); + fprintf(afp, + " %8.4e %15.5f %15.5f %10.5f %10.5f %10.5e " + " %i\n", + i * dt * timefac, Tavg, Pavg, gc, Z, Vol * VolFac, N); + + printf("\n TO ANIMATE YOUR SIMULATION, OPEN THE FILE \n '%s' WITH VMD " + "AFTER THE SIMULATION COMPLETES\n", + tfn); + printf("\n TO ANALYZE INSTANTANEOUS DATA ABOUT YOUR MOLECULE, OPEN THE FILE " + "\n " + " '%s' WITH YOUR FAVORITE TEXT EDITOR OR IMPORT THE DATA INTO EXCEL\n", + ofn); + printf("\n THE FOLLOWING THERMODYNAMIC AVERAGES WILL BE COMPUTED AND " + "WRITTEN TO THE FILE \n '%s':\n", + afn); + printf("\n AVERAGE TEMPERATURE (K): %15.5f\n", Tavg); + printf("\n AVERAGE PRESSURE (Pa): %15.5f\n", Pavg); + printf("\n PV/nT (J * mol^-1 K^-1): %15.5f\n", gc); + printf("\n PERCENT ERROR of pV/nT AND GAS CONSTANT: %15.5f\n", + 100 * fabs(gc - 8.3144598) / 8.3144598); + printf("\n THE COMPRESSIBILITY (unitless): %15.5f \n", Z); + printf("\n TOTAL VOLUME (m^3): %10.5e \n", Vol * VolFac); + printf("\n NUMBER OF PARTICLES (unitless): %i \n", N); + + fclose(tfp); + fclose(ofp); + fclose(afp); + + return 0; +} + +void initialize() { + int n, p, i, j, k; + double pos; + + // Number of atoms in each direction + n = int(ceil(pow(N, 1.0 / 3))); + + // spacing between atoms along a given direction + pos = L / n; + + // index for number of particles assigned positions + p = 0; + // initialize positions + for (i = 0; i < n; i++) { + for (j = 0; j < n; j++) { + for (k = 0; k < n; k++) { + if (p < N) { + + r[p][0] = (i + 0.5) * pos; + r[p][1] = (j + 0.5) * pos; + r[p][2] = (k + 0.5) * pos; + } + p++; + } + } + } + + // Call function to initialize velocities + initializeVelocities(); + + /*********************************************** + * Uncomment if you want to see what the initial positions and velocities + are printf(" Printing initial positions!\n"); for (i=0; i= N) { +// break; +// } +// double quot, rnorm, term1, term2; +// +// fourD rj = load_4d(r[j + k]); +// fourD rij = sub_4d(ri, rj); +// fourD distTmp = mul_4d(rij, rij); +// rij4[k] = rij; +// +// fourD temp = hadd_4d(distTmp, distTmp); +// twoD lo = get_lower_2d(temp); +// twoD hi = get_upper_2d(temp); +// twoD sum = add_2d(lo, hi); +// +// // Convert the scalar result to a double +// double finalSum; +// store_lower_1d(&dist[k], sum); +// } +// fourD dists = load_4d(dist); +// fourD quot = div_4d(create_4d(sigma * sigma), dists); +// fourD term2 = mul_4d(quot, mul_4d(quot, quot)); +// fourD Pots = mul_4d(create_4d(epsilon_8), mul_4d(term2, sub_4d(term2, create_4d(1.)))); +// // Perform horizontal addition and store the result in a scalar +// fourD temp = hadd_4d(Pots, Pots); +// twoD lo = get_lower_2d(temp); +// twoD hi = get_upper_2d(temp); +// twoD sum = add_2d(lo, hi); +// +// // Convert the scalar result to a double +// double finalSum; +// store_lower_1d(&finalSum, sum); +// Pot += finalSum; +// +// fourD distSqd = mul_4d(dists, mul_4d(dists, dists)); +// fourD rSqd_inv7 = mul_4d(distSqd, mul_4d(distSqd, dists)); +// fourD f8 = div_4d(sub_4d(create_4d(48.), mul_4d(create_4d(24.), distSqd)), rSqd_inv7); +// +// // Go back to the original loop +// for (int k = 0; k < numParts; k++) { +// if (j + k >= N) { +// break; +// } +// fourD tmp = mul_4d(rij4[k], create_4d(f8[k])); +// fourD aI = load_4d(a[i]); +// fourD aJ = load_4d(a[j + k]); +// fourD sum = add_4d(aI, tmp); +// fourD sub = sub_4d(aJ, tmp); +// store_4d(a[i], sum); +// store_4d(a[j + k], sub); +// } +// } +// } +// //} +// +// return Pot; +// } + +double PotentialAndAcceleration(double dt) { + memset(a, 0, sizeof(a)); + double Pot = 0.; + # pragma omp parallel for reduction(+:Pot,a) + for (int i = 0; i < N - 1; i++) { + double ai0 = 0., ai1 = 0., ai2 = 0.; + double rI[3] = {r[i][0], r[i][1], r[i][2]}; + for (int j = i + 1; j < N; j++) { + double quot, term2; + // component-by-componenent position of i relative to j + double rij[3]; + // sum of squares of the components + double rSqd = 0.; + + for (int k = 0; k < 3; k++) { + double rijk = rI[k] - r[j][k]; + + rij[k] = rijk; + + rSqd += rijk * rijk; + } + + // Here we remove the pow function and simplify the calculation + double rSqd_3 = rSqd * rSqd * rSqd; + double rSqd_7 = rSqd_3 * rSqd_3 * rSqd; + double f = (48. - (24. * rSqd_3)) / rSqd_7; + // from F = ma, where m = 1 in natural units! + double tmp = rij[0] * f; + double tmp1 = rij[1] * f; + double tmp2 = rij[2] * f; + ai0 += tmp; + ai1 += tmp1; + ai2 += tmp2; + a[j][0] -= tmp; + a[j][1] -= tmp1; + a[j][2] -= tmp2; + + quot = sigma * sigma / rSqd; + term2 = quot * quot * quot; + Pot += term2 * (term2 - 1.); + } + a[i][0] += ai0; + a[i][1] += ai1; + a[i][2] += ai2; + } + return Pot*epsilon_8; +} + +// Function to calculate the potential energy of the system +double Potential() { + double quot, rSqd, rnorm, term1, term2, Pot; + int i, j; + + Pot = 0.; + + for (i = 0; i < N - 1; i++) { + for (j = i + 1; j < N; j++) { + rSqd = 0.; + double rI[3] = {r[i][0], r[i][1], r[i][2]}; + for (int k = 0; k < 3; k++) { + double rijk = rI[k] - r[j][k]; + rSqd += rijk * rijk; + } + + quot = sigma * sigma / rSqd; + term2 = quot * quot * quot; + Pot += epsilon_8 * term2 * (term2 - 1.); + } + } + return Pot; +} + +// Uses the derivative of the Lennard-Jones potential to calculate +// the forces on each atom. Then uses a = F/m to calculate the +// accelleration of each atom. +void computeAccelerations() { + double f, rSqd, tmp = 0.; + memset(a, 0, sizeof(a)); + + for (int i = 0; i < N - 1; i++) { // loop over all distinct pairs i,j + double rI[3] = {r[i][0], r[i][1], r[i][2]}; + for (int j = i + 1; j < N; j++) { + // component-by-componenent position of i relative to j + double rij[3]; + // sum of squares of the components + double rSqd = 0.; + + for (int k = 0; k < 3; k++) { + double rijk = rI[k] - r[j][k]; + + rij[k] = rijk; + + rSqd += rijk * rijk; + } + + // Here we remove the pow function and simplify the calculation + double rSqd_3 = rSqd * rSqd * rSqd; + double rSqd_7 = rSqd_3 * rSqd_3 * rSqd; + double f = (48. - (24. * rSqd_3)) / rSqd_7; + // from F = ma, where m = 1 in natural units! + for (int k = 0; k < 3; k++) { + double tmp = rij[k] * f; + a[i][k] += tmp; + a[j][k] -= tmp; + } + } + } +} + +// returns sum of dv/dt*m/A (aka Pressure) from elastic collisions with walls +double VelocityVerlet(double dt, int iter, double *PE, FILE *fp) { + int i, j, k; + + double psum = 0.; + + // Compute accelerations from forces at current position + // this call was removed (commented) for predagogical reasons + // computeAccelerations(); + // Update positions and velocity with current velocity and acceleration + // printf(" Updated Positions!\n"); + for (i = 0; i < N; i++) { + for (j = 0; j < 3; j++) { + double tmp = 0.5 * a[i][j] * dt; + r[i][j] += v[i][j] * dt + tmp * dt; + + v[i][j] += tmp; + } + // printf(" %i %6.4e %6.4e %6.4e\n",i,r[i][0],r[i][1],r[i][2]); + } + // Update accellerations from updated positions + // computeAccelerations (); + *PE = PotentialAndAcceleration(dt); + // Update velocity with updated acceleration + for (i = 0; i < N; i++) { + for (j = 0; j < 3; j++) { + v[i][j] += 0.5 * a[i][j] * dt; + } + } + + // Elastic walls + for (i = 0; i < N; i++) { + for (j = 0; j < 3; j++) { + if (r[i][j] < 0.) { + v[i][j] *= -1.; //- elastic walls + psum += 2 * m * fabs(v[i][j]) / dt; // contribution to pressure + // from "left" walls + } + if (r[i][j] >= L) { + v[i][j] *= -1.; //- elastic walls + psum += 2 * m * fabs(v[i][j]) / dt; // contribution to pressure + // from "right" walls + } + } + } + + /* removed, uncomment to save atoms positions */ + /*for (i=0; i= 1.0 || rsq == 0.0); + + fac = sqrt(-2.0 * log(rsq) / rsq); + gset = v1 * fac; + available = true; + + return v2 * fac; + } else { + + available = false; + return gset; + } +}