| kspaceFirstOrder3D-OMP 1.0 The C++ implementation of the k-wave toolbox for the time-domain simulation of acoustic wave fields in 3D

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kspaceFirstOrder3D-OMP

## 1 Overview

k-Wave is an open source MATLAB toolbox designed for the time-domain simulation of propagating acoustic waves in 1D, 2D, or 3D. The toolbox has a wide range of functionality, but at its heart is an advanced numerical model that can account for both linear or nonlinear wave propagation, an arbitrary distribution of weakly heterogeneous material parameters, and power law acoustic absorption (http://www.k-wave.org).

This project is a part of the k-Wave toolbox accelerating 3D simulations using an optimized C++ implementation to run moderate to big grid sizes. Compiled binaries of the C++ code for x86 architectures are available from (http://www.k-wave.org/download). Both 64-bit Linux (Ubuntu / Debian) and 64-bit Windows versions are provided. This Doxygen documentation was created based on the Linux version and provides details on the implementation of the C++ code.

## 2 Compilation

The source codes of `kpsaceFirstOrder3D-OMP` are written using the C++03 standard and the OpenMP 2.0 library. There are variety of different C++ compilers that can be used to compile the source codes. We recommend using either the GNU C++ compiler (gcc/g++) version 4.3 and higher, or the Intel C++ compiler version 11.0 and higher. The codes can be compiled on 64-bit Linux and Windows. 32-bit systems are not supported. This section describes the compilation procedure using GNU and Intel compilers on Linux. (The Windows users are encouraged to download the Visual Studio 2010 project and compile it using Intel Compiler from within Visual Studio.)

Before compiling the code, it is necessary to install a C++ compiler and several libraries. The GNU compiler is usually part of Linux distributions and distributed as open source. It can be downloaded from http://gcc.gnu.org/ if necessary. The Intel compiler can be downloaded from http://software.intel.com/en-us/intel-composer-xe/. This package also includes the Intel MKL (Math Kernel Library) library that contains FFT. The Intel compiler is only free for non-commercial use.

The code also relies on several libraries that is to be installed before compiling:

- HDF5 library - Mandatory I/O library, version 1.8 or higher (http://www.hdfgroup.org/HDF5/).
- FFTW library - Optional library for FFT, version 3.0 or higher (http://www.fftw.org/).
- MKLlibrary - Optional library for FFT, version 11.0 or higher (http://software.intel.com/en-us/intel-composer-xe/).

Although it is possible to use any combination of the FFT library and the compiler, the best performance is observed when using GNU compiler and FFTW, or Intel Compiler and Intel MKL.

2.1 The HDF5 library installation procedure

1. Download the 64-bit HDF5 library package for your platform (http://www.hdfgroup.org/HDF5/release/obtain5.html).

2. Configure the HDF5 distribution. Enable the high-level library and specify an installation folder by typing:

            ./configure --enable-hl --prefix=folder_to_install

3. Make the HDF library by typing:

            make

4. Install the HDF library by typing:

    	make install

2.2 The FFTW library installation procedure

1. Download the FFTW library package for your platform (http://www.fftw.org/download.html).

2. Configure the FFTW distribution. Enable OpenMP support, SSE instruction set, single precision data type, and specify an installation folder:

            ./configure --enable-single --enable-sse --enable-openmp --enable-shared --prefix=folder_to_install

if you intend to use the FFTW library (and the C++ code) only on a selected machine and want to get the best possible performance, you may also add processor specific optimisations and AVX instructions set. Note, the compiled binary code is not likely to be portable on different CPUs (e.g. even from Intel Sandy Bridge to Intel Nehalem).

            ./configure --enable-single --enable-avx --enable-openmp  --enable-shared --with-gcc-arch=<arch> --prefix=folder_to_install

More information about the installation and customization can be found at http://www.fftw.org/fftw3_doc/Installation-and-Customization.htm.

3. Make the FFTW library by typing:

    	make

4. Install the FFTW library by typing:

    	make install

2.3 The Intel Compiler and MKL installation procedure

1. Download the Intel Composer XE package for your platform (http://software.intel.com/en-us/intel-compilers).

2. Run the installation script and follow the procedure by typing:

    	./install.sh

2.4 Compiling the C++ code

When the libraries and the compiler have been installed, you are ready to compile the `kspaceFirstOrder3D-OMP` code.

1. Download the `kspaceFirstOrder3D-OMP` souce codes.

2. Open the `Makefile` file. The Makefile supports code compilation under GNU compiler and FFTW, or Intel compiler with MKL. Uncomment the desired compiler by removing the character of ``#`'.

    	#COMPILER = GNU
    	#COMPILER = Intel

3. Select how to link the libraries. Static linking is preferred, however, on some systems (HPC clusters) it may be better to use dynamic linking and use the system specific library at runtime.

    	#LINKING = STATIC
    	#LINKING = DYNAMIC

4. Set installation paths of the libraries (an example is shown bellow).

    	FFT_DIR=/usr/local
    	MKL_DIR=/opt/intel/composer_xe_2011_sp1/mkl
    	HDF5_DIR=/usr/local/hdf5-1.8.9

5. The code will be built to work on all CPUs implementing the Streaming SSE2 instruction set (Intel Pentium IV, AMD Athlon XP 64 and newer). Higher performance may be obtained by providing more information about the target CPU (SSE 4.2 instructions, AVX instruction, architecture optimization). For more detail, check on the compiler documentation.

6. Compile the source code by typing:

            make

If you want to clean the distribution, type:

            make clean

## 3 Command Line Parameters

The C++ code requires two mandatory parameters and accepts a few optional parameters and flags. The mandatory parameters `-i` and `-o` specify the input and output file. The file names respect the path conventions for particular operating system. If any of the files is not specified, cannot be found or created, an error message is shown.

The `-t` parameter sets the number of threads used, which defaults the system maximum. On CPUs with Intel Hyper-Threading (HT), performance will generally be better if HT is disabled in the BIOS settings. If HT is switched on, the default will be to create twice as many threads as there are physical processor cores, which might slow down the code execution. Therefore, if the HT is on, try specifying the number of threads manually for best performance (e.g., 4 for Intel Quad-Core). We recommend experimenting with this parameter to find the best configuration. Note, if there are other tasks being executed on the system, it might be useful to further limit the number of threads to prevent system overload.

The `-r` parameter specifies how often information about the simulation progress is printed to the command line. By default, the C++ code prints out the progress of the simulation, the elapsed time, and the estimated time of completion in intervals corresponding to 5% of the total number of times steps.

The `-c` parameter specifies the compression level used by the ZIP library to reduce the size of the output file. The actual compression rate is highly dependent on the shape of the sensor mask and the range of stored quantities. In general, the output data is very hard to compress, and using higher compression levels can greatly increase the time to save data while not having a large impact on the final file size. The default compression level of 3 represents a balance between compression ratio and performance that is suitable in most cases.

The `--benchmark` parameter enables the total length of simulation (i.e., the number of time steps) to be overwritten by setting a new number of time steps to simulate. This is particularly useful for performance evaluation and benchmarking. As the code performance is relatively stable, 50-100 time steps is usually enough to predict the simulation duration. This parameter can also be used to quickly find the ideal number of CPU threads to use.

The `-h` and `--help` parameters print all the parameters of the C++ code, while the `--version` parameter reports the code version and internal build number.

The remaining flags specify the output quantities to be recorded during the simulation and stored on disk analogous to the sensor.record input. If the `-p` or `--p` raw flags are set (these are equivalent), a time series of the acoustic pressure at the grid points specified by the sensor mask is recorded. If the `--p` rms and/or `--p` max flags are set, the root mean square and/or maximum values of the pressure at the grid points specified by the sensor mask are recorded. Finally, if the `--p` final flag is set, the values for the entire acoustic pressure field in the final time step of the simulation is stored (this will always include the PML, regardless of the setting for ``PMLInside'` ). Flags to record the acoustic particular velocity are defined in an analogous fashion.

In addition to returning the acoustic pressure and particle velocity, the acoustic intensity at the grid points specified by the sensor mask can also be calculated and stored. To account for the staggered grid scheme, approximate values for the particle velocity at the unstaggered grid points are automatically calculated using linear interpolation before multiplication by the acoustic pressure. Two means of aggregation are possible: `-I` or `--I_avg` calculates and stores the average acoustic intensity, while `--I` max calculates the maximum acoustic intensity.

Any combination of `p`, `u` and `I` fags is admissible. If no output flag is set, a time-series for the acoustic pressure is recorded. If it is not necessary to collect the output quantities over the entire simulation, the starting time step when the collection begins can be specified using the -s parameter. Note, the index for the first time step is 1 (this follows the MATLAB indexing convention).

    ---------------------------------- Usage ---------------------------------
    Mandatory parameters:
      -i <input_file_name>            : HDF5 input file
      -o <output_file_name>           : HDF5 output file

    Optional parameters:
      -t <num_threads>                : Number of CPU threads (default = MAX)
      -r <interval_in_%>              : Progress print interval (default = 5%)
      -c <comp_level>                 : Output file compression level <0,9>
                                          (default = 3)
      --benchmark <steps>             : Run a specified number of time steps

      -h                              : Print help
      --help                          : Print help
      --version                       : Print version

    Output flags:
      -p                              : Store acoustic pressure
                                          (default if nothing else is on)
                                          (the same as --p_raw)
      --p_raw                         : Store raw time series of p (default)
      --p_rms                         : Store rms of p
      --p_max                         : Store max of p
      --p_final                       : Store final pressure field

      -u                              : Store ux, uy, uz
                                          (the same as --u_raw)
      --u_raw                         : Store raw time series of ux, uy, uz
      --u_rms                         : Store rms of ux, uy, uz
      --u_max                         : Store max of ux, uy, uz
      --u_final                       : Store final acoustic velocity

      -I                              : Store intensity
                                          (the same as --I_avg)
      --I_avg                         : Store avg of intensity
      --I_max                         : Store max of intensity

      -s <timestep>                   : Time step when data collection begins
                                          (default = 1)
    --------------------------------------------------------------------------

## 4 HDF5 File Structure

The C++ code has been designed as a standalone application which is not dependent on MATLAB libraries or a MEX interface. This is of particular importance when using servers and supercomputers without MATLAB support. For this reason, simulation data must be transferred between the C++ code and MATLAB using external input and output files. These files are stored using the Hierarchical Data Format HDF5 (http://www.hdfgroup.org/HDF5/). This is a data model, library, and file format for storing and managing data. It supports a variety of datatypes, and is designed for flexible and efficient I/O and for high volume and complex data. The HDF5 technology suite includes tools and applications for managing, manipulating, viewing, and analysing data in the HDF5 format.

Each HDF5 file is a container for storing a variety of scientific data and is composed of two primary types of objects: groups and datasets. A HDF5 group is a structure containing zero or more HDF5 objects, together with supporting metadata. A HDF5 group can be seen as a disk folder. A HDF5 dataset is a multidimensional array of data elements, together with supporting metadata. A HDF5 dataset can be seen as a disk file. Any HDF5 group or dataset may also have an associated attribute list. A HDF5 attribute is a user-defined HDF5 structure that provides extra information about a HDF5 object. More information can be obtained from the HDF5 documentation (http://www.hdfgroup.org/HDF5/doc/index.html).

The HDF5 input file for the C++ simulation code contains a file header with brief description of the simulation stored in string attributes, and the root group `/' which stores all the simulation properties in the form of 3D datasets (a complete list of input datasets is given in Appendix B). The HDF5 output file contains a file header with the simulation description as well as performance statistics, such as the simulation time and memory consumption, stored in string attributes. The results of the simulation are stored in the root group `/' in the form of 3D datasets.

    ==============================================================================================================
                                            Input File Header
    =============================================================================================================
    created_by                              Short description of the tool that created this file
    creation_date                           Date when the file was created
    file_description                        Short description of the content of the file (e.g. simulation name)
    file_type                               Type of the file (input)
    major_version                           Major version of the file definition (1)
    minor_version                           Minor version of the file definition (0)
    ==============================================================================================================

    ==============================================================================================================
                                            Output File Header
    ==============================================================================================================
    created_by                              Short description of the tool that created this file
    creation_date                           Date when the file was created
    file_description                        Short description of the content of the file (e.g. simulation name)
    file_type                               Type of the file (output)
    major_version                           Major version of the file definition (1)
    minor_version                           Minor version of the file definition (0)
    -------------------------------------------------------------------------------------------------------------
    host_names                              List of hosts (computer names) the simulation was executed on
    number_of_cpu_cores                     Number of CPU cores used for the simulation
    data_loading_phase_execution_time       Time taken to load data from the file
    pre-processing_phase_execution_time     Time taken to pre-process data
    simulation_phase_execution_time         Time taken to run the simulation
    post-processing_phase_execution_time    Time taken to complete the post-processing phase
    total_execution_time                    Total execution time
    peak_core_memory_in_use                 Peak memory required per core during the simulation
    total_memory_in_use Total               Peak memory in use
    ==============================================================================================================

All input and output parameters are stored as three dimensional datasets with dimension sizes designed by `(Nx, Ny, Nz)`. In order to support scalars and 1D and 2D arrays, the unused dimensions are set to 1 . For example, scalar variables are stored with a dimension size of `(1,1,1)`, 1D vectors oriented in y-direction are stored with a dimension size of `(1, Ny, 1)`, and so on. If the dataset stores a complex variable, the real and imaginary parts are stored in an interleaved layout and the lowest used dimension size is doubled (i.e., Nx for a 3D matrix, Ny for a 1D vector oriented in the y-direction). The datasets are physically stored in row-major order (in contrast to column-major order used by MATLAB) using either the ``H5T_IEEE_F32LE'` data type for floating point datasets or ``H5T_STD_U64LE'` for integer based datasets.

In order to enable compression of big datasets (3D variables, output time series), selected datasets are not stored as monolithic blocks but broken into chunks that are compressed by the ZIP library and stored separately. The chunk size is defined as follows:

- `(Nx, Ny, 1)` in the case of 3D variables (one 2D slab).
- `(N_sensor_points, 1, 1)` in the case of the output time series (one time step of the simulation).

All datasets have two attributes that specify the content of the dataset. The ``data_type'` attribute specifies the data type of the dataset. The admissible values are either ``float'` or ``long'`. The ``domain_type'` attribute specifies the domain of the dataset. The admissible values are either ``real'` for the real domain or ``complex'` for the complex domain. The C++ code reads these attributes and checks their values.

    ==============================================================================================================
                                            Input File Datasets
    ==============================================================================================================
    Name                            Size           Data type       Domain Type      Condition of Presence
    ==============================================================================================================
      1. Simulation Flags
    --------------------------------------------------------------------------------------------------------------
      ux_source_flag                (1, 1, 1)       long            real
      uy_source_flag                (1, 1, 1)       long            real
      uz_source_flag                (1, 1, 1)       long            real
      p_source_flag                 (1, 1, 1)       long            real
      p0_source_flag                (1, 1, 1)       long            real
      transducer_source_flag        (1, 1, 1)       long            real
      nonuniform_grid_flag          (1, 1, 1)       long            real            must be set to 0
      nonlinear_flag                (1, 1, 1)       long            real
      absorbing_flag                (1, 1, 1)       long            real
    --------------------------------------------------------------------------------------------------------------
      2. Grid Properties
    --------------------------------------------------------------------------------------------------------------
      Nx                            (1, 1, 1)       long            real
      Ny                            (1, 1, 1)       long            real
      Nz                            (1, 1, 1)       long            real
      Nt                            (1, 1, 1)       long            real
      dt                            (1, 1, 1)       float           real
      dx                            (1, 1, 1)       float           real
      dy                            (1, 1, 1)       float           real
      dz                            (1, 1, 1)       float           real
    --------------------------------------------------------------------------------------------------------------
      3 Medium Properties
    --------------------------------------------------------------------------------------------------------------
      3.1 Regular Medium Properties

      rho0                          (Nx, Ny, Nz)    float         real              heterogenous
      		           	(1, 1, 1)       float         real              homogenous
      rho0_sgx                      (Nx, Ny, Nz)    float         real              heterogenous
                                    (1, 1, 1)       float         real              homogenous
      rho0_sgy                      (Nx, Ny, Nz)    float         real              heterogenous
                                    (1, 1, 1)       float         real              homogenous
      rho0_sgz                      (Nx, Ny, Nz)    float         real              heterogenous
    				(1, 1, 1)       float         real              homogenous
      c0                            (Nx, Ny, Nz)    float         real              heterogenous
      		       		(1, 1, 1)       float         real              homogenous
      c_ref                         (1, 1, 1)       float         real

      3.2 Nonlinear Medium Properties (defined if (nonlinear_flag == 1))

      BonA                          (Nx, Ny, Nz)    float         real              heterogenous
                                    (1, 1, 1)       float         real              homogenous

      3.3 Absorbing Medium Properties (defined if (absorbing_flag == 1))

      alpha_coef                    (Nx, Ny, Nz)    float         real              heterogenous
                                    (1, 1, 1)       float         real              homogenous
      alpha_power                   (1, 1, 1)       float         real
    --------------------------------------------------------------------------------------------------------------
      4. Sensor Variables
    --------------------------------------------------------------------------------------------------------------
    sensor_mask_index               (Nsens, 1, 1)   long          real
    --------------------------------------------------------------------------------------------------------------
      5 Source Properties
    --------------------------------------------------------------------------------------------------------------
      5.1 Velocity Source Terms (defined if (ux_source_flag == 1 || uy_source_flag == 1 || uz_source_flag == 1))

      u_source_mode                 (1, 1, 1)          long       real
      u_source_many                 (1, 1, 1)          long       real
      u_source_index                (Nsrc, 1, 1)       long       real
      ux_source_input               (1, Nt_src, 1)     float      real              u_source_many == 0
                                    (Nsrc, Nt_src, 1)  float      real              u_source_many == 1
      uy_source_input               (1, Nt_src,  1)    float      real              u_source_many == 0
                                    (Nsrc, Nt_src, 1)  float      real              u_source_many == 1
      uz_source_input               (1, Nt_src, 1)     float      real              u_source_many == 0
                                    (Nt_src, Nsrc, 1)  float      real              u_source_many == 1

      5.2 Pressure Source Terms (defined if p_source_flag == 1))

      p_source_mode                 (1, 1, 1)          long       real
      p_source_many                 (1, 1, 1)          long       real
      p_source_index                (Nsrc, 1, 1)       long       real
      p_source_input                (Nsrc, Nt_src, 1)  float      real              p_source_many == 1
                                    (1, Nt_src, 1)     float      real              p_source_many == 0

      5.3 Transducer Source Terms (defined if (transducer_source_flag == 1))

      u_source_index        	(Nsrc, 1, 1)    long          real
      transducer_source_input       (Nt_src, 1, 1)  float         real
      delay_mask			(Nsrc, 1, 1)    float         real

      5.4 IVP Source Terms (defined if ( p0_source_flag ==1)

      p0_source_input               (Nx, Ny, Nz)    float         real

    --------------------------------------------------------------------------------------------------------------
      6. K-space and Shift Variables
    --------------------------------------------------------------------------------------------------------------
      ddx_k_shift_pos_r     	(Nx/2 + 1, 1, 1)  float       complex
      ddx_k_shift_neg_r             (Nx/2 + 1, 1, 1)  float       complex
      ddy_k_shift_pos               (1, Ny, 1)        float       complex
      ddy_k_shift_neg               (1, Ny, 1)        float       complex
      ddz_k_shift_pos               (1, 1, Nz)        float       complex
      ddz_k_shift_neg               (1, 1, Nz)        float       complex
    --------------------------------------------------------------------------------------------------------------
      7. PML Variables
    --------------------------------------------------------------------------------------------------------------
      pml_x_size                    (1, 1, 1)       long          real
      pml_y_size                    (1, 1, 1)       long          real
      pml_z_size                    (1, 1, 1)       long          real
      pml_x_alpha                   (1, 1, 1)       float         real
      pml_y_alpha                   (1, 1, 1)       float         real
      pml_z_alpha                   (1, 1, 1)       float         real

      pml_x                         (Nx, 1, 1)      float         real
      pml_x_sgx                     (Nx, 1, 1)      float         real
      pml_y                         (1, Ny, 1)      float         real
      pml_y_sgy                     (1, Ny, 1)      float         real
      pml_z                         (1, 1, Nz)      float         real
      pml_z_sgz                     (1, 1, Nz)      float         real
    ==============================================================================================================

    ==============================================================================================================
                                            Output File Datasets
    ==============================================================================================================
    Name                            Size           Data type        Domain Type     Condition of Presence
    ==============================================================================================================
      1. Simulation Flags
    --------------------------------------------------------------------------------------------------------------
      ux_source_flag                (1, 1, 1)       long          real
      uy_source_flag                (1, 1, 1)       long          real
      uz_source_flag                (1, 1, 1)       long          real
      p_source_flag                 (1, 1, 1)       long          real
      p0_source_flag                (1, 1, 1)       long          real
      transducer_source_flag        (1, 1, 1)       long          real
      nonuniform_grid_flag          (1, 1, 1)       long          real
      nonlinear_flag		(1, 1, 1)       long          real
      absorbing_flag		(1, 1, 1)       long          real
      u_source_mode                 (1, 1, 1)       long          real              if u_source
      u_source_many                 (1, 1, 1)       long          real              if u_source
      p_source_mode                 (1, 1, 1)       long          real              if p_source
      p_source_many                 (1, 1, 1)       long          real              if p_source

    --------------------------------------------------------------------------------------------------------------
      2. Grid Properties
    --------------------------------------------------------------------------------------------------------------
      Nx                            (1, 1, 1)       long          real
      Ny                            (1, 1, 1)       long          real
      Nz                            (1, 1, 1)       long          real
      Nt                            (1, 1, 1)       long          real
      dt                            (1, 1, 1)       float         real
      dx                            (1, 1, 1)       float         real
      dy                            (1, 1, 1)       float         real
      dz                            (1, 1, 1)       float         real
    -------------------------------------------------------------------------------------------------------------
      3. PML Variables
    --------------------------------------------------------------------------------------------------------------
      pml_x_size                    (1, 1, 1)       long          real
      pml_y_size                    (1, 1, 1)       long          real
      pml_z_size                    (1, 1, 1)       long          real
      pml_x_alpha                   (1, 1, 1)       float         real
      pml_y_alpha                   (1, 1, 1)       float         real
      pml_z_alpha                   (1, 1, 1)       float         real

      pml_x                         (Nx, 1, 1)      float         real
      pml_x_sgx                     (Nx, 1, 1)      float         real
      pml_y                         (1, Ny, 1)      float         real
      pml_y_sgy                     (1, Ny, 1)      float         real
      pml_z                         (1, 1, Nz)      float         real
      pml_z_sgz                     (1, 1, Nz)      float         real
    --------------------------------------------------------------------------------------------------------------
      4. Simulation Results
    --------------------------------------------------------------------------------------------------------------

      p                             (Nsens, Nt - s, 1) float      real              -p or --p_raw
      p_rms                         (Nsens, 1, 1)      float      real              --p_rms
      p_max                         (Nsens, 1, 1)      float      real              --p_max
      p_final                       (Nx, Ny, Nz)       float      real              --p_final

      ux                            (Nsens, Nt - s, 1) float      real              -u or --u_raw
      uy                            (Nsens, Nt - s, 1) float      real              -u or --u_raw
      uz                            (Nsens, Nt - s, 1) float      real              -u or --u_raw

      ux_rms                        (Nsens, 1, 1)      float      real              --u_rms
      uy_rms                        (Nsens, 1, 1)      float      real              --u_rms
      uz_rms                        (Nsens, 1, 1)      float      real              --u_rms

      ux_max                        (Nsens, 1, 1)      float      real              --u_max
      uy_max                        (Nsens, 1, 1)      float      real              --u_max
      uz_max                        (Nsens, 1, 1)      float      real              --u_max

      ux_final                      (Nx, Ny, Nz)       float      real              --u_final
      uy_final                      (Nx, Ny, Nz)       float      real              --u_final
      uz_final                      (Nx, Ny, Nz)       float      real              --u_final

      Ix_avg                        (Nsens, 1, 1)      float      real              -I or --I_avg
      Iy_avg                        (Nsens, 1, 1)      float      real              -I or --I_avg
      Iz_avg                        (Nsens, 1, 1)      float      real              -I or --I_avg

      Ix_max                        (Nsens, 1, 1)      float      real              --I_max
      Iy_max                        (Nsens, 1, 1)      float      real              --I_max
      Iz_max                        (Nsens, 1, 1)      float      real              --I_max
    ==============================================================================================================

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