SCTL: Scientific Computing Template Library

SCTL is a header-only C++ library providing various functionalities for scientific computing. This documentation outlines these functionalities and provides a guide to getting started.

Requirements

The only requirement to use SCTL is a working C++11 compliant compiler with OpenMP 4.0 support. It has been tested with GCC-9 and newer.

Getting Started

To get started, download the latest version of SCTL from the SCTL GitHub.

git clone https://github.com/dmalhotra/SCTL.git

Since SCTL is a header-only library, it does not require compilation or installation. Simply include the sctl.hpp header file in your C++ project and start using the provided classes and functions.

#include <sctl.hpp>

Ensure the compiler can locate the header file by providing the path to SCTL_ROOT/include using the flag -I ${SCTL_ROOT}/include.

Optional Dependencies

The following libraries can be optionally used when available. If not available, SCTL uses its own implementation which may be slower.

• BLAS: Enable by defining SCTL_HAVE_BLAS.
• LAPACK: Enable by defining SCTL_HAVE_LAPACK.
• libmvec: Enable by defining SCTL_HAVE_LIBMVEC.
• Intel SVML: Enable by defining SCTL_HAVE_SVML.
• MPI: Enable by defining SCTL_HAVE_MPI (see Comm).
• FFTW: Enable double precision by defining SCTL_HAVE_FFTW, single precision by defining SCTL_HAVE_FFTWF, or long double precision by defining SCTL_HAVE_FFTWL (see FFT).
• PVFMM: Enable by defining SCTL_HAVE_PVFMM (requires MPI, see ParticleFMM).

To enable support for any of these libraries, define the corresponding flag during compilation. For example, to enable MPI support, use -DSCTL_HAVE_MPI.

Optional Compiler Flags

The following compiler flags can be used to enable or disable specific features in SCTL:

• -DSCTL_MEMDEBUG: Enable memory debugging (iterator.hpp, static-array.hpp).
• -DSCTL_GLOBAL_MEM_BUFF=<size in MB>: Use a global memory buffer for allocations.
• -DSCTL_PROFILE: Enable profiling.
• -DSCTL_VERBOSE=<level>: Enable verbose profiling output.
• -DSCTL_SIG_HANDLER: Enable stack trace.
• -DSCTL_QUAD_T: Enable support for quad-precision type.

Features and Capabilities

The following list outlines the primary features and capabilities provided by the library, along with references to detailed tutorials and documentation for each component:

• Basic Data Structures: Fundamental classes for storing and manipulating data.

  • Vector: Dynamically allocated linear array.
  • Matrix, Permutation: Dynamically allocated 2D array for matrix operations.
  • Tensor: Statically allocated multi-dimensional array.

• Numerical Solvers and Algorithms: Methods for solving equations, performing interpolations, numerical integration, and partitioning data.

  • SDC (Spectral Deferred Correction): High-order solver for ordinary differential equations.
  • GMRES solver, Krylov preconditioner: Distributed memory GMRES solver.
  • LagrangeInterp: Polynomial interpolation and differentiation.
  • ChebQuadRule, LegQuadRule: Clenshaw-Curtis and Gauss-Legendre quadrature rules.
  • InterpQuadRule: Generating special quadrature rules.
  • Tree, PtTree, Morton: Morton order based N-dimensional parallel tree structure.

• Spectral Methods: Methods for spectral representations and transformations.

  • FFT: Wrapper for FFTW to perform fast Fourier transforms.
  • SphericalHarmonics: Computing spherical harmonics.

• Boundary Integral Methods: Techniques for solving partial differential equations using boundary integral representations.

  • BoundaryIntegralOp: Generic class for instantiating layer-potential operators.
  • Kernel functions: Contains a variety of kernel functions for integral equations.
  • ParticleFMM: Integration with PVFMM for particle N-body calculations.

• High Performance Computing (HPC): Tools for parallel and distributed computing.

  • Comm: Wrapper for MPI to facilitate parallel computing.
  • Vec: SIMD vectorization class for optimized computations.
  • OpenMP utilities: Parallel algorithms such as merge-sort and scan using OpenMP.
  • Profile: Tools for profiling and performance analysis.

• Utilities: Miscellaneous utilities for data handling, debugging, and visualization.

  • VTUData: Writes unstructured VTK files for data visualization.
  • QuadReal, basic math functions: Quad-precision type and essential mathematical functions.
  • Iterator, ConstIterator, StaticArray: Iterator and static array utilities.
  • MemoryManager: Aligned memory allocation and deallocation.
  • Stacktrace utility: Prints stack traces for debugging.
  • GEMM, SVD (unoptimized): Provides basic implementations of GEMM and SVD operations.

• Legacy (Unmaintained): Older functionalities that are no longer actively maintained.

  • Boundary quadrature: Boundary integrals on quad-patches using hedgehog quadrature.
  • ChebBasis: Tensor product Chebyshev basis for general-dimension computations.