README.md

LSS2 (Linear System Solvers) - migrated from LSS

Linear System Solvers library. Written in C++17. It contains a few wrappers around CUDA cuSolver library functions plus some other well known solvers. It also contains some ODE and PDE solvers.

ODE Solver

• general 2nd degree two-point equation with variable coefficients (supports all Dirichlet, Neumann, Robin boundary conditions)
• All solvers support uniform and non-uniform grid with variable scaling

PDE Solver

• 1D general heat equation with variable coefficients (in space and time dimension) (supports all Dirichlet, Neumann, Robin boundary conditions)
• 1D general wave equation with variable coefficients (in space and time dimension) (supports all Dirichlet, Neumann, Robin boundary conditions)
• 2D general Heston type model with variable coefficients (in space and time dimension) (support for Douglas-Rachford ADI, Craig-Sneyd ADI, Modified Craig-Sneyd ADI, Hundsdorfer-Verwer ADI)
• 3D general Heston-Hull-White type model with variable coefficients (in space and time dimension) (support for Douglas-Rachford ADI so far) - only experimental and not yet released in DLLs (to be released soon..)
• All solvers support uniform and non-uniform grid with variable scaling

Requirement

• Library is being developed in VS2019 for win-x64 arch
• NVIDIA CUDA lib >= v11.3

Usage

Visual Studio:

0.step

Make sure to create CUDA project (>= v11.3) in VS

1.step

Open property pages for the newly created project and

1. under Debugging set Environment to point to CUDA binaries folder (in my case it is PATH=C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v11.3\bin)
2. under VC++ Directories set Include Directories to point to include folder of this library
3. under VC++ Directories set Library Directories to point to lib folder of this library
4. under Linker|Input add to Additional Dependencies cusolver.lib;cusparse.lib; cublas.lib; cublasLt.lib;lss2_debug.lib (or lss2_release.lib in case of Release configuration)
5. under Linker|General set Additional Library Dependencies to point to lib folder of this library
6. under CUDA Linker|General set Additional Library Directories to point to lib folder of this library

2.step

Place lss2_debug.dll,lss2_debug.lib (lss2_release.dll, lss2_release.lib in case of Release configuration) into your executable folder

3.step

Now you should be ready to use the library. Test it using following example

// main.cu file 


#include <iostream>
#include <string>
#include <lss/utilities/range.hpp>
#include <lss/configs/discretization_config_1d.hpp>


int main()
{

    // number of space subdivisions:
    std::size_t const Sd = 100;
    // number of time subdivisions:
    std::size_t const Td = 100;
    // space range:
    auto const &space_range_ptr = lss::range_builder().lower(0.0).upper(20.0).build();
    // time range
    auto const &time_range_ptr = lss::range_builder().lower(0.0).upper(1.0).build();

    //// discretization config:
    auto const &discretization_ptr = lss::discretization_config_1d_builder()
                                        .space_range(space_range_ptr)
                                        .number_of_space_points(Sd)
                                        .time_range(time_range_ptr)
                                        .number_of_time_points(Td)
                                        .build();

    std::cout<<"Uniform space step value: "<< discretization_ptr->space_step()<<"\n";

    return 0;
}

Output

• results can be put into stream or xml. Folder output also contains some python scripts that parse the resulting xmls and plot the solutions.

Some curves from ODE solver

Simple Two-point BVP (u''(x) = -2 with Dirichlet and Robin BC)

Some surfaces from PDE solver

Heat equation (Dirichlet BC) from implicit solver

Wave equation (Dirichlet BC) from implicit solver

Wave equation (Neumann BC) from implicit solver

Damped wave equation (Dirichlet BC) from implicit solver

Advection equation from implicit solver

Black-Scholes equation from implicit solver

Heston equation DR from implicit solver

Heston Barrier equation DR from implicit solver

Heston equation MCS from implicit solver

Heston equation HV from implicit solver

SABR equation from implicit solver

Heston equation from explicit solver

SABR dynamics

Heston-Hull-White dynamics for specific rate r_0

Heston-Hull-White dynamics for specific rate r_1

Heston-Hull-White dynamics for specific vol v_0

Heston-Hull-White dynamics for specific vol v_1

Heston-Hull-White dynamics for specific vol s_0

Heston-Hull-White dynamics for specific vol s_1