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twomass.cpp
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twomass.cpp
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#include <iostream>
#include <cmath>
#include <blaze/Blaze.h>
#include <blaze/math/Submatrix.h>
#include <blaze/Forward.h>
using namespace std;
using namespace blaze;
using blaze::unaligned;
using blaze::DynamicVector ;
// ASSEMBLY func of element matrices
// assembly matrix : project m,k to M,K according to the element unit LM((1,2), (2,3)) ---> index ((0,1),(1,2))
DynamicMatrix<double> getGlobalMatrix(const size_t &a, DynamicMatrix<double> &X, DynamicMatrix<double> &x ){ // nel, M0, m0
for(size_t i = 0UL; i <a; i++){
for(size_t j = 0UL; j<a; j++){
X(i,j) = X(i,j) + x(i,j);
}
}
for(size_t i = 1UL; i <= a; i++){
for(size_t j = 1UL; j<= a; j++){
X(i,j) = X(i,j) + x(i-1,j-1);
}
}
return X;
}
// diagnoal matrice
DynamicMatrix<double> diagMatrix(DynamicMatrix<double> Y){
DynamicMatrix<double> D(3UL, 3UL);
for(size_t i = 0UL; i <Y.rows(); i++){
for(size_t j = 0UL; j< Y.columns(); j++){
if(i == j){
D(i,j) = Y(i,j);
}else{
D(i,j) = 0;
}
}
}
return D;
}
int main()
{
// 1. (given)initial parameters for two spring obj.
// *** ...INPUT DATA...
const double m1 = 6.0, m2 = 3.0;
const double k1 = 0.1667, k2 = 0.1667;
const size_t nsd = 1; // Number of space dimensions
const size_t ndof = 1; // Number of degrees of freedom per node (1D)
const size_t nel = 2; // number of element
const size_t nnp = nel+1; // total number of node 3
const int nen = 2; // nodes on each element
// Initialize vector of displacement,velocity , accelaration: d0, d_v, d_a : use vector???
DynamicVector<double,columnVector > d{ 0, 6, 12 }; //displacement0
DynamicVector<double> v(3UL); // Initialize velocity vector
const int nd = 1; // Number of prescribed displacement degrees-of-freedom
// ZeroVector<double> d_v(3UL); // column vec // velocity0
// ZeroVector<double> d_a(3UL); // accelaration0
// define element unit |--|--| i.e. 0--1--2 (unit1: node1-> node2; unit2: node2->node3)
StaticMatrix<int,2UL,2UL> LM{{0,1}, {1,2}}; // did not use LM array to calculate the M, K
// *** ...TIME ITERATION...
const double dt = 0.01; // define the time step size
const int nt = 8000; // the number of time steps
// NEWMARK PARAMETERS
double beta_b = 0.25;
double gamma_b = 0.5;
//////////////
// 2. discretization, object -> elements
// m, k vector for each element
// note: skip calculate process
// generate element mass matrix
DynamicMatrix<double> mel( 2UL , 2UL ); // mel from calculating(FEM), here just assign it a matrix
mel = {{3.0, 0},
{0, 3.0}};
// generate element stiffness matrix
DynamicMatrix<double> k( 2UL , 2UL ); // mel from calculating(FEM), here just assign it a matrix
k = { { 0.1667, -0.1667},
{ -0.1667, 0.1667 }};
// define APPLIED FORCE
//fd=zeros(nnp,nt+1);
// ZeroVector<double> fd(nnp, nt+1);
DynamicMatrix <double> fd(nnp, nt+1);
fd(2, 0) = 1.0; // fd(3,1) = 1 --> project to c++ index rule : fd(2,0) = 1
// fd.set( 2, 0, 1 );
//////////////////////////////////////////////////////////////
// 3. assembly of global matrix
// [m] --> [M]; [k] -->[K]
// initialize global M vector ---(use dynamic matrix in blaze)
DynamicMatrix<double> M(nel+1 , nel+1);
// initialize global K vector ---(use dynamic matrix in blaze)
DynamicMatrix<double> K(nel+1 , nel+1);
// assembly of global matrix function
M = getGlobalMatrix(nel, M, mel);
K = getGlobalMatrix(nel, K, k);
// 4. split matrix: Partitioning
// Partition M
DynamicMatrix<double> L_m, U_m, P_m;
DynamicMatrix<double> D_m(3UL, 3UL);
lu( M, U_m, L_m, P_m); // decomposition M, get L_m, U_m
D_m = diagMatrix(M);
// std::cout << "L_m:"<< L_m <<std::endl;
// std::cout << "U_m:"<< U_m <<std::endl;
// std::cout << "D_m:"<< D_m <<std::endl;
// Partition K
DynamicMatrix<double> L_k, U_k, P_k; //DynamicMatrix<double> means DynamicMatrix<double,rowMajor> ==> so lu(k,u,l)
lu(K, U_k, L_k, P_k);
DynamicMatrix<double> D_k(3UL, 3UL);
D_k = diagMatrix(K);
// **... get K, M _plus and minus matrices
// for jacobi:
DynamicMatrix<double> M_plus_j, M_minus_j, K_plus_j, K_minus_j;
M_plus_j = D_m;
M_minus_j = -(L_m + U_m);
K_plus_j = D_k;
K_minus_j = K_plus_j - K;
//K_minus_j = -(L_k + U_k);
std::cout << "K_plus_j:"<< K_plus_j <<std::endl;
std::cout << "K_minus_j:"<< K_minus_j <<std::endl;
// for Gaus_seidel:
DynamicMatrix<double> M_plus_g, M_minus_g, K_plus_g, K_minus_g;
// cout << "M size -" << size(M) << endl;
//cout << "D_m size " << size(D_m) << endl;
// cout << "L_m " << size(L_m) << endl;
M_plus_g = D_m + L_m;
M_minus_g = -(U_m);
K_plus_g = D_k + L_k;
K_minus_g = -(U_k);
// Starting solving
//****************************************************************************//
// Jacobi
// 1. get initial d_0, v_0, a_0;
DynamicVector<double,columnVector > d_0, v_0, a_0, a0;
d_0=d;
v_0=v;
//take the initial displacement and the associated initial istantaneous acceleration as I.C. (not for the analytical solution
// a0=M\(-K*d);
DynamicVector<double,columnVector> temp = -K * d;
a0 = inv(M) * temp; // -K * d is a vector;
a0[0] = 0;
a_0=a0;
// 2. set initial d,v,a for the whole process
DynamicMatrix <double> U_d(nnp, nt+1); // use zeroMatrix<>(), got complain
DynamicMatrix <double> U_v(nnp, nt+1);
DynamicMatrix <double> U_a(nnp, nt+1);
// std::cout << "U_d:"<< U_d <<std::endl;
/*
U_d(:,1)=d;
U_v(:,1)=v;
U_a(:,1)=a0;
*/
// initialize first column
for( size_t i=0UL; i<nnp; ++i ) {
U_d(i,0) = d[i];
U_v(i,0) = v[i];
U_a(i,0) = a0[i];
}
//Iniziatise WR time-discrete matrix (initial WRs=initial conditions)
DynamicMatrix <double> WR(nnp, nt+1);
DynamicMatrix <double> WR2(nnp, nt+1);
DynamicMatrix <double> WRv(nnp, nt+1);
DynamicMatrix <double> WRa(nnp, nt+1);
for( size_t i=0UL; i<nnp; ++i ) {
for( size_t j=0UL; j<nt+1; ++j ) {
WR(i,j)= d[i];
WRv(i,j) = v[i];
WRa(i,j) = a0[i];
}
}
// Initialize first row of WR_STOR=ITERATION 0, THEN COMPARED WITH ITERATION %1!
/*
WR_STOR(1,:)=WR(nnp,:);
WR_STOR2(1,:)=WR2(nnp,:);
*/
DynamicMatrix<double> WR_STOR(nnp, nt+1);
DynamicMatrix<double> WR_STOR2(nnp, nt+1);
int STOR_line = 0;
for( size_t j=0UL; j<nt+1; ++j ) {
WR_STOR(0,j) = WR(2,j);
WR_STOR2(0,j) = WR2(2,j);
}
// initialize e (error) and the counting i
size_t e=1;
size_t e2=1;
size_t i = 0;
DynamicVector<double,columnVector > a(nnp);
while(e>pow(10,-14) || e2>pow(10,-14)){
d = d_0;
v = v_0;
a = a0;
// SOLUTION OF THE MATRIX SYSTEM: vector force
DynamicMatrix <double> fd1(nnp, nt+1);
//DynamicMatrix<double> temp(nnp, 1);
for( size_t jj=0UL; jj<nt+1; ++jj ) {
// fd1(ii,jj) = K_minus_j * WR(ii, jj); per ogni colonna di WR (spostamento a un t moltiplico per Kminus che � come moltiplicare per l'1/6 di prima (coeff riduttivo/moltiplicativo))
submatrix(fd1, 0UL, jj, 3UL, 1UL) = K_minus_j * submatrix(WR, 0UL, jj, 3UL, 1UL);
// std::cout<< "fd1: " << fd1(0,0)<<std::endl;
// std::cout<< "fd1: " << fd1(1,0)<<std::endl;
// std::cout<< "fd1: " << fd1(2,0)<<std::endl;
// break;
}
//SOLUTION
DynamicMatrix<double,columnMajor> A;
A = M + beta_b *(dt*dt)*K_plus_j;
DynamicMatrix<double,columnMajor> L, U, P;
lu(A, L, U, P);
DynamicVector<double, columnVector> d1p(nnp, 1UL);
DynamicVector<double> v1p(nnp, 1UL);
// PREDICTOR PHASE // ?????? d1p, v1p didnt change as n increment, so move it outside of while
d1p = d + dt*v + ((dt*dt)/2) * (1-2*beta_b)*a;
v1p = v + (1-gamma_b)*dt*a;
// for(size_t i=0UL; i<nnp; ++i){
// d1p[i] = d[i] + dt*v[i] + ((dt*dt)/2) * (1-2*beta_b)*a[i];
// v1p[i] = v[i] + (1-gamma_b)*dt*a[i];
// }
std::cout << "d1p " << d1p<< std::endl;
int n = 0;
while(n<nt){
//SOLUTION : disp('b')
// DynamicMatrix <double> fd1(nnp, nt+1);
// DynamicMatrix<double> M_plus_j
DynamicVector<double,columnVector> b(nnp);
b = column(fd1, n+1) - K_plus_j * d1p;
// LU_decomposition
DynamicVector<double,columnVector > z(nnp);
DynamicVector<double,columnVector > a1(nnp);
z = inv(L) * b;
a1 = inv(U) * z;
a1[0] = 0;
// CORRECTOR PHASE
DynamicVector<double,columnVector > d1(nnp);
DynamicVector<double,columnVector > v1(nnp);
d1 = d1p + beta_b * (dt*dt)*a1;
v1 = v1p+(1-gamma_b)*dt*a1;
/**
* SUBSTITUTING
U_d(:,n+1)=d1;
U_v(:,n+1)=v1;
U_a(:,n+1)=a1;
*/
for( size_t i=0UL; i<nnp; ++i ) {
U_d(i,n+1) = d1[i];
U_v(i,n+1) = v1[i];
U_a(i,n+1) = a1[i];
}
d = d1;
v = v1;
a = a1;
for( size_t i=0UL; i<nnp; ++i ) {
WR(i,n+1) = d1[i];
WRv(i,n+1) = v1[i];
WRa(i,n+1) = a1[i];
}
n++;
}
i = i+1;
cout <<"J current i: " << i << endl;
STOR_line = STOR_line + 1;
cout <<" STOR_line : " << STOR_line << endl;
// WR_STOR(STOR_line,:) = WR(nnp,:);
for( size_t j=0UL; j<nt+1; ++j ) {
WR_STOR(STOR_line,j) = WR(2,j);
}
DynamicMatrix <double> cc(1UL, nt+1);
for( size_t j=0UL; j<nt+1; ++j ) {
cc(0,j) = WR_STOR(STOR_line,j) - WR_STOR(STOR_line-1,j);
}
// cc=WR_STOR(STOR_line,:)-WR_STOR(STOR_line-1,:);
DynamicMatrix <double> dd(1, nt+1);
dd = abs(cc);
e = max(dd);
std::cout << "e " << e << std::endl;
// WR_STOR2
for( size_t j=0UL; j<nt+1; ++j ) {
WR_STOR2(STOR_line,j) = WR(1,j);
}
DynamicMatrix <double> cc2(1, nt+1);
for( size_t j=0UL; j<nt+1; ++j ) {
cc2(0,j) = WR_STOR2(STOR_line,j) - WR_STOR2(STOR_line-1,j);
}
// cc=WR_STOR(STOR_line,:)-WR_STOR(STOR_line-1,:);
DynamicMatrix <double> dd2(1, nt+1);
dd2 = abs(cc2);
e2 = max(dd2);
std::cout << "e2 " << e2 << std::endl;
}
}