splines made but need to be checked, solver seems to make wrong results

This commit is contained in:
Vasco C. B. Ferreira
2026-03-14 00:21:42 +01:00
parent dce1ff364e
commit f2ee1606b7
6 changed files with 395 additions and 102 deletions
+54
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@@ -0,0 +1,54 @@
#ifndef NUFI_BLAS_HPP
#define NUFI_BLAS_HPP
#include <cstddef>
/*!
* \brief Convenience wrappers for BLAS, with overloads for single and double
* precision.
*/
namespace blas
{
double dot( const size_t n, const double *x, size_t incx,
const double *y, size_t incy );
float dot( const size_t n, const float *x, size_t incx,
const float *y, size_t incy );
void axpy( size_t n, double alpha, const double *x, size_t incx,
double *y, size_t incy );
void axpy( size_t n, float alpha, const float *x, size_t incx,
float *y, size_t incy );
void scal( size_t n, double alpha, double *x, size_t incx );
void scal( size_t n, float alpha, float *x, size_t incx );
void copy( size_t n, const double *x, size_t incx, double *y, size_t incy );
void copy( size_t n, const float *x, size_t incx, float *y, size_t incy );
void ger( const size_t M, const size_t N, const double alpha,
const double *X, const size_t incX, const double *Y, const size_t incY,
double *A, const size_t lda);
void ger( const size_t M, const size_t N, const float alpha,
const float *X, const size_t incX, const float *Y, const size_t incY,
float *A, const size_t lda);
void gemv( const char trans, size_t m, size_t n,
double alpha, const double *a, size_t lda,
const double *x, size_t incx, double beta,
double *y, size_t incy );
void gemv( const char trans, size_t m, size_t n,
float alpha, const float *a, size_t lda,
const float *x, size_t incx, float beta,
float *y, size_t incy );
}
#endif
+11 -12
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@@ -4,6 +4,8 @@
#include <cmath>
#include <deal.II/base/function.h>
#include "parameters.hpp"
#include "splines.hpp"
#include "lsmr.hpp"
using namespace dealii;
@@ -36,8 +38,8 @@ inline double compute_rho(const double x,
}
template <typename real, size_t order, size_t dx = 0>
real eval( real x, const real *coeffs) noexcept
template <size_t dx = 0>
double eval(double x, const double *coeffs) noexcept
{
using std::floor;
@@ -48,7 +50,7 @@ real eval( real x, const real *coeffs) noexcept
x = x - Parameters::LX * floor( x/Parameters::LX );
// Knot number
real x_knot = floor( x/Parameters::SPLINE_DX);
double x_knot = floor( x/Parameters::SPLINE_DX);
size_t ii = static_cast<size_t>(x_knot);
@@ -56,10 +58,10 @@ real eval( real x, const real *coeffs) noexcept
x = x/Parameters::SPLINE_DX - x_knot;
// Scale according to derivative.
real factor = 1;
double factor = 1;
for ( size_t i = 0; i < dx; ++i ) factor *= 1/Parameters::SPLINE_DX;
return factor*splines1d::eval<real,order,dx>( x, coeffs + ii );
return factor*splines1d::eval<double,Parameters::SPLINE_ORDER,dx>(x, coeffs + ii);
}
template <typename real, size_t order>
@@ -72,17 +74,15 @@ void interpolate( real *coeffs, const real *values) // Least Squares needs to be
struct mat_t // STRUCT AND CONFIG NEEDS TO BE REVIEWED
{
const config_t<real> &config;
real N[ order ];
mat_t( const config_t<real> &conf ): config { conf }
mat_t()
{
splines1d::N<real,order>(0,N);
}
void operator()( const real *in, real *out ) const
{
#pragma omp parallel for
for ( size_t i = 0; i < Parameters::SPLINE_NX; ++i )
{
real result = 0;
@@ -103,10 +103,9 @@ void interpolate( real *coeffs, const real *values) // Least Squares needs to be
struct transposed_mat_t // STRUCT AND CONFIG NEEDS TO BE REVIEWED
{
const config_t<real> &config;
real N[ order ];
transposed_mat_t( const config_t<real> &conf ): config { conf }
transposed_mat_t()
{
splines1d::N<real,order>(0,N);
}
@@ -132,9 +131,9 @@ void interpolate( real *coeffs, const real *values) // Least Squares needs to be
}
};
mat_t M { config }; transposed_mat_t Mt { config };
mat_t M; transposed_mat_t Mt;
lsmr_options<real> opt; opt.silent = true;
lsmr( config.Nx, config.Nx, M, Mt, values, tmp.get(), opt );
lsmr( Parameters::SPLINE_NX, Parameters::SPLINE_NX , M, Mt, values, tmp.get(), opt );
if ( opt.iter == opt.max_iter )
std::cerr << "Warning. LSMR did not converge.\n";
+252
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@@ -0,0 +1,252 @@
#ifndef LSMR_HPP
#define LSMR_HPP
#include <cmath>
#include <limits>
#include <iomanip>
#include <iostream>
#include "blas.hpp"
template <typename real>
struct lsmr_options
{
///////////
// INPUT //
///////////
// Whether to print messages to std::cout.
bool silent = true;
// Residual of normal equations AᵀAx = Aᵀb
bool relative_residual = true;
real target_residual = std::numeric_limits<real>::epsilon();
size_t max_iter = 1000;
// How many Lánczos vectors to keep for local reorthogonalisation.
// Choose zero for no reorthogonalisation, pure LSMR.
// Choose a large value for complete reorthognalisation.
//
// In an ideal world without roundoff errors, this would have no effect
// at all, as the Lánczos vectors would be perfectly orthogonal. In practice
// this property is lost rather quickly. One may choose to store some of
// the most recent Lánczos vectors to enforce this property manually. This
// increase convergence speed at the cost of additional memory requirements.
size_t reorthogonalise_u = 50;
size_t reorthogonalise_v = 50;
////////////
// OUTPUT //
////////////
// Iteration count and reached residual.
// Estimates of ‖A‖ and cond(A)
size_t iter; real residual;
real norm_A_estimate, cond_estimate;
};
template <typename real, typename mat, typename transposed_mat>
void lsmr( size_t m, size_t n, const mat& A, const transposed_mat& At,
const real *b, real *x, lsmr_options<real> &S );
namespace lsmr_impl
{
template <typename real>
real norm( size_t n, const real *x )
{
using std::hypot;
real result = 0;
for ( size_t i = 0; i < n; ++i )
result = hypot(result,x[i]);
return result;
}
// Reorthognalise u with respect to the previous vectors in buffer,
// using the modified GramSchmidt process. Overwrite the oldest vector
// in buffer when full.
template <typename real>
void reorthogonalise( real *buf, size_t n, size_t buffer_max,
real *u, size_t iter )
{
using std::min;
using blas::dot;
using blas::axpy;
using blas::scal;
using blas::copy;
size_t n_buffered = min( iter+1, buffer_max );
for ( size_t i = 0; i < n_buffered; ++i )
{
real fac = -dot( n, u, 1, buf + i*n, 1 );
axpy( n, fac, buf + i*n, 1, u, 1 );
}
scal( n, 1/norm(n,u), u, 1 );
copy( n, u, 1, buf + ((iter+1)%buffer_max)*n, 1 );
}
}
template <typename real, typename mat, typename transposed_mat>
void lsmr( size_t m, size_t n, const mat& A, const transposed_mat& At,
const real *b, real *x, lsmr_options<real> &S )
{
using std::min;
using std::max;
using std::abs;
using std::swap;
using std::hypot;
using blas::axpy;
using blas::scal;
using blas::copy;
using lsmr_impl::norm;
using lsmr_impl::reorthogonalise;
// Allocation of buffers.
size_t max_buf = min(n,m)-1;
S.reorthogonalise_u = min(S.reorthogonalise_u,max_buf);
S.reorthogonalise_v = min(S.reorthogonalise_v,max_buf);
size_t u_buffer_size = max( S.reorthogonalise_u, size_t(1) );
size_t v_buffer_size = max( S.reorthogonalise_v, size_t(1) );
std::unique_ptr<real[]> data { new real[ n*( 4 + v_buffer_size ) +
m*( 2 + u_buffer_size ) ] {} };
real *u = data.get();
real *utmp = u + m;
real *ubuf = utmp + m;
real *v = ubuf + m*u_buffer_size;
real *vtmp = v + n;
real *h = vtmp + n;
real *h_bar = h + n;
real *vbuf = h_bar + n;
At(b,v);
const real norm_ATb = norm(n,v);
A(x,u); axpy(m,real(-1),b,1,u,1);
scal(m, real(-1), u, 1 ); // u = b - Ax;
real alpha = 0;
real beta = norm(m,u);
if ( beta > real(0) )
{
scal(m, real(1)/beta, u, 1 ); // u = b - Ax / norm(b-Ax)
At(u,v); // v = At*u
alpha = norm(n,v);
}
if ( alpha > real(0) )
scal(n, real(1)/alpha, v, 1 ); // v = At*u/norm(At*u)
copy(n,u,1,ubuf,1); // u_buf.col(0) = u_buf
copy(n,v,1,vbuf,1); // v_buf.col(0) = v
copy(n,v,1,h,1); // h = v
if ( alpha * beta == real(0) ) return;
real alpha_bar = alpha, zeta_bar = alpha*beta;
real rho = 1, rho_bar = 1, c_bar = 1, s_bar = 0;
real c, s, theta, zeta, theta_bar, rho_prev, rho_bar_prev;
// For estimating the condition number.
real sigma_max = 0, sigma_min = std::numeric_limits<real>::max();
real rho_bar_max = 0, rho_bar_min = std::numeric_limits<real>::max();
S.norm_A_estimate = 0;
for ( S.iter = 0; S.iter < S.max_iter; ++S.iter )
{
// Continue the bidiagonalisation.
A(v,utmp); axpy(m,-alpha,u,1,utmp,1); swap(u,utmp); // u = A*v - alpha*u
beta = norm(m,u);
if ( beta > 0 )
{
scal(m, real(1)/beta, u, 1 );
if ( S.reorthogonalise_u )
reorthogonalise( ubuf, m, u_buffer_size, u, S.iter );
S.norm_A_estimate = hypot( alpha, S.norm_A_estimate );
S.norm_A_estimate = hypot( beta , S.norm_A_estimate );
At(u,vtmp); axpy(n,-beta,v,1,vtmp,1); swap(v,vtmp); // v = At*u - beta*v
alpha = norm(n,v);
if ( alpha > 0 )
{
scal(n,real(1)/alpha, v, 1 );
if ( S.reorthogonalise_v )
reorthogonalise( vbuf, n, v_buffer_size, v, S.iter );
}
}
// Construct and apply rotation P_k
rho_prev = rho;
rho = hypot(alpha_bar,beta);
c = alpha_bar/rho;
s = beta/rho;
theta = s*alpha;
alpha_bar = c*alpha;
// Construct and apply rotation \bar{P}_k
rho_bar_prev = rho_bar;
if ( S.iter )
{
rho_bar_max = max( rho_bar, rho_bar_max );
rho_bar_min = min( rho_bar, rho_bar_min );
}
theta_bar = s_bar*rho;
rho_bar = hypot( c_bar*rho, theta );
if ( S.iter )
{
sigma_max = max( rho_bar_max, c_bar*rho );
sigma_min = min( rho_bar_min, c_bar*rho );
}
c_bar = c_bar * rho/rho_bar;
s_bar = theta/rho_bar;
zeta = c_bar * zeta_bar;
zeta_bar = -s_bar*zeta_bar;
// Update h, h_bar, x
scal(n, -(theta_bar*rho)/(rho_prev*rho_bar_prev), h_bar, 1 ) ;
axpy(n, real(1), h, 1, h_bar, 1 ); // h_bar = h - factor*h_bar
axpy( n, zeta/(rho*rho_bar), h_bar, 1, x, 1 ); // x += factor * h_bar
scal(n, -theta/rho, h, 1 );
axpy(n, real(1), v, 1, h, 1 ); // h = v - factor*h;
// Estimate quantities.
if ( S.relative_residual ) S.residual = abs(zeta_bar)/norm_ATb;
else S.residual = abs(zeta_bar);
S.cond_estimate = sigma_max / sigma_min;
if ( S.residual <= S.target_residual )
{
if ( S.silent == false )
{
std::cout << "LSMR: Iteration: " << std::setw(4) << S.iter << ", "
<< "Residual: " << std::setw(12) << std::scientific << S.residual << ", "
<< "cond estimate: " << std::setw(12) << std::scientific << S.cond_estimate << ".\n";
}
return;
}
if ( S.silent == false && (S.iter%10) == 0 )
{
std::cout << "LSMR: Iteration: " << std::setw(4) << S.iter << ", "
<< "Residual: " << std::setw(12) << std::scientific << S.residual << ", "
<< "cond estimate: " << std::setw(12) << std::scientific << S.cond_estimate << ".\n";
}
}
}
#endif
+62 -76
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@@ -8,15 +8,14 @@
#include <deal.II/numerics/fe_field_function.h>
#include <iostream>
#include <memory>
#include <ostream>
#include <vector>
#include <cstddef>
#include "parameters.hpp"
#include "poisson_problem.hpp"
#include "fields.hpp" // holds f0(x,v), and compute_rho(x)
#include "spline_field.hpp" // old GPT splines
#include "splines.hpp" //new splines
#include "fields.hpp"
using namespace dealii;
@@ -26,15 +25,15 @@ public:
NuFISolver();
void run();
double eval_rho(unsigned int n, double x, const std::vector<double> E_coeffs, unsigned int Nv = Parameters::NV);
double eval_ftilda(unsigned int n, double x, double u, const std::vector<double> E_coeffs);
void save_ftilda(unsigned int n, const std::vector<double> E_coeffs, unsigned int Nx_out, unsigned int Nv_out, const std::string &filename);
double eval_rho(unsigned int n, double x, const double *E_coeffs, unsigned int Nv = Parameters::NV);
double eval_ftilda(unsigned int n, double x, double u, const double *E_coeffs);
void save_ftilda(unsigned int n, const double *E_coeffs, unsigned int Nx_out, unsigned int Nv_out, const std::string &filename);
private:
unsigned int Nt = std::floor(Parameters::TMAX/Parameters::DT);
[[maybe_unused]] unsigned int Nx = Parameters::SPLINE_NX;
unsigned int Nx = Parameters::SPLINE_NX;
double Lx = Parameters::LX;
@@ -42,8 +41,6 @@ private:
unsigned int order;
double dt = Parameters::DT;
PoissonProblem<1> poisson;
};
@@ -51,72 +48,82 @@ private:
inline double NuFISolver::eval_ftilda(unsigned int n,
double x,
double u,
const std::vector<double> E_coeffs)
const double *E_coeffs)
{
double Lu = std::abs(Parameters::V_DOMAIN_LEFT - Parameters::V_DOMAIN_RIGHT);
if ( n == 0 ) return f0(x,u);
if (n == 0)
return f0(x, u);
const size_t stride_x = 1;
const size_t stride_t = stride_x*(Parameters::SPLINE_NX + Parameters::SPLINE_ORDER - 1);
// Initial half-step.
u += 0.5*dt*E_spline.eval(x);
double Ex;
const double *c;
// We omit the initial half-step.
while ( --n )
{
x -= dt*u;
u += dt*E_spline.eval(x);
x = x - Parameters::DT *u;
c = E_coeffs + n*stride_t;
Ex = -eval<1>(x, c);
u = u + Parameters::DT *Ex;
}
// Final half-step.
x -= dt*u;
u += 0.5*dt*E_spline.eval(x);
// The final half-step.
x -= Parameters::DT*u;
c = E_coeffs + n*stride_t;
Ex = -eval<1>(x, c);
u += 0.5*Parameters::DT*Ex;
double x_periodic = x - Lx * std::floor(x / Lx);
double u_periodic = u - Lu * std::floor(u / Lu);
return f0(x_periodic, u_periodic);
return f0(x,u);
}
inline double NuFISolver::eval_rho(const unsigned int n,
const double x,
const std::vector<double> E_coeffs,
const double *E_coeffs,
const unsigned int Nv)
{
const double dv = (Parameters::V_DOMAIN_RIGHT - Parameters::V_DOMAIN_LEFT) / Nv;
const double v_min = Parameters::V_DOMAIN_LEFT;
double integral = 0.0;
for (unsigned int i = 0; i < Nv; ++i)
{
const double v = Parameters::V_DOMAIN_LEFT + (i + 0.5) * dv;
AssertThrow(std::isfinite(E_spline.eval(x)), ExcMessage("NaN detected in E_spline.eval(x) inside NuFISolver::eval_rho integral loop"));
integral += eval_ftilda(n, x, v, E_spline) * dv;
}
integral += eval_ftilda(n, x, v_min + i * dv, E_coeffs) * dv;
return 1.0 - integral;
}
class ChargeDensity_NuFI : public Function<1>
template<unsigned int dim>
class ChargeDensity_NuFI : public Function<dim>
{
public:
ChargeDensity_NuFI(NuFISolver &solver, size_t n, const std::vector<double> E_coeffs)
: solver(solver), n(n), E_coeffs(E_coeffs) {}
ChargeDensity_NuFI(const double *rho_values, unsigned int Nx)
: Function<dim>(), rho(rho_values), Nx(Nx) {}
virtual double value(const Point<1> &p,
virtual double value(const Point<dim> &p,
[[maybe_unused]] const unsigned int component = 0) const override
{
double x = p[0];
const double x = p[0];
return solver.eval_rho(n, x, E_coeffs);
// Map x -> grid index
const double L = Parameters::LX;
const double dx = L / (Nx-1);
int i = static_cast<int>(std::floor((x - Parameters::X_DOMAIN_LEFT) / dx));
// periodic wrap
i = (i % Nx + Nx) % Nx;
return rho[i];
}
private:
NuFISolver &solver;
size_t n;
const std::vector<double> E_coeffs;
const double *rho;
const unsigned int Nx;
};
inline void NuFISolver::save_ftilda(unsigned int n,
const std::vector<double> E_coeffs,
const double *E_coeffs,
unsigned int Nx_out,
unsigned int Nv_out,
const std::string &filename)
@@ -144,7 +151,7 @@ inline void NuFISolver::save_ftilda(unsigned int n,
{
double v = vmin + (j + 0.5)*dv;
double val = eval_ftilda(n, x, v, E_spline);
double val = eval_ftilda(n, x, v, E_coeffs);
file << val;
@@ -160,60 +167,39 @@ inline void NuFISolver::save_ftilda(unsigned int n,
inline void NuFISolver::run()
{
std::cout << "Start of NuFISolver::run()\n\n";
std::cout << "Building E_sline\n\n";
// init E_spline
using std::abs;
using std::max;
unsigned int Nx = Parameters::SPLINE_NX;
// Nx grid points
double dx = Lx / (Nx-1);
const size_t stride_t = Nx + order - 1;
std::vector<double> E_grid(Nx);
std::unique_ptr<double[]> coeffs { new double[ Nt*stride_t ] {} };
std::unique_ptr<double,decltype(std::free)*> rho { reinterpret_cast<double*>(std::aligned_alloc(64,sizeof(double)*Nx)), std::free };
//set initial E points
for (unsigned int i=0; i<Nx; ++i)
{
[[maybe_unused]] double x = Parameters::X_DOMAIN_LEFT + i*dx;
E_grid[i] = 0;
}
std::vector<double> E_coeffs(E_grid, Parameters::X_DOMAIN_LEFT, Parameters::X_DOMAIN_RIGHT); // Needs correction
if ( rho == nullptr ) throw std::bad_alloc {};
for (unsigned int it = 0; it < Nt; ++it)
{
std::cout << "Timestep " << it << " / " << Nt << std::endl << std::endl;
// Step 1: Evaluate rho^n(x) using current E_spline
rho.resize(Nx);
for (unsigned int i = 0; i < (Nx); ++i)
// compute rho
for(size_t i = 0; i<Nx; i++)
{
double x = (i + 0.5) * dx;
rho[i] = eval_rho(it, x, E_spline, Parameters::NV);
}
ChargeDensity_NuFI rho_function(*this, it, E_spline);
poisson.set_rhs_function(rho_function);
for (unsigned int i=0; i< rho.size(); ++i) // check for bad rho[i]
{
AssertThrow(std::isfinite(rho[i]), ExcMessage("NaN detected in rho"));
double ith_rho = eval_rho(it, i, coeffs.get(), Parameters::NV);
AssertThrow(std::isfinite(ith_rho), ExcMessage("NaN detected in rho"));
rho.get()[i] = ith_rho;
}
poisson.set_rhs_function(std::make_unique<ChargeDensity_NuFI<1>>(rho.get(), Parameters::SPLINE_NX));
poisson.solve_step();
if (it % Parameters::PLOT_FREQUENCY == 0)
{
std::cout << "Saving results... \n\n";
save_ftilda(it, E_spline, 128, 128, "results/ftilda_" + std::to_string(it) + ".dat");
save_ftilda(it, coeffs.get(), 128, 128, "results/ftilda_" + std::to_string(it) + ".dat");
poisson.output_results(it);
}
E_grid = poisson.sample_electric_field(poisson, Nx, 0.0, Lx);
E_spline = std::vector<double> E_coeffs; // needs correction
}
std::cout << "NuFI simulation finished.\n";
+3
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@@ -3,6 +3,7 @@
#include <cmath>
#include <cstdlib>
namespace Parameters
{
constexpr unsigned int DIMENSION = 1;
@@ -27,9 +28,11 @@ namespace Parameters
constexpr double DT=1./16.;
constexpr unsigned int TMAX = 10;
//spline options
constexpr int SPLINE_NX = 512;
constexpr double SPLINE_DX = LX/SPLINE_NX;
constexpr size_t SPLINE_ORDER = 4;
//Plotting options
constexpr int PLOT_FREQUENCY = 2;
+6 -7
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@@ -33,7 +33,9 @@
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/fe_field_function.h>
#include <memory>
#include <string>
#include <utility>
#include <vector>
#include "parameters.hpp"
@@ -53,7 +55,7 @@ public:
void solve_step();
void run();
void set_rhs_function(const Function<dim> &rhs);
void set_rhs_function(std::unique_ptr<Function<dim>> rhs_function);
const Vector<double> &get_solution() const { return solution; }
const DoFHandler<dim> &get_dof_handler() const { return dof_handler; }
@@ -83,7 +85,7 @@ private:
Vector<double> solution; // phi
Vector<double> system_rhs;
const Function<dim> *rhs_function;
std::unique_ptr<const Function<dim>> rhs_function;
MappingQ<dim> mapping;
};
@@ -91,9 +93,9 @@ private:
// Utilities
template <int dim>
void PoissonProblem<dim>::set_rhs_function(const Function<dim> &rhs)
void PoissonProblem<dim>::set_rhs_function(std::unique_ptr<Function<dim>> rhs)
{
rhs_function = &rhs;
rhs_function = std::move(rhs);
}
template <int dim>
@@ -214,9 +216,6 @@ public:
}
};
// =-=-=-=-= Poisson equation solver =-=-=-=-=
template <int dim>
void PoissonProblem<dim>::assemble_system()
{