Extensions to k-Wave toolbox used for ultrasound modelling are described. Aim of extensions is to reduce time and space complexity by presenting alternative representations of tissues and transducers in simulation. This project clarifies basic principles and features of k-Wave, describes design of new representations and finally describes implementation of the suggested extensions.

The work deals with design and implementation of 2D ultrasound simulation. Applications of the ultrasound simulation can be found in medicine, biophysic or image reconstruction. As an example of using the ultrasound simulation we can mention High Intensity Focused Ultrasound that is used for diagnosing and treating cancer. The program is part of the k-Wave toolbox designed for supercomputer systems, specifically for machines with shared memory architecture. The program is implemented in the C++ language and using OpenMP acceleration.  Using the designed solution, it is possible to solve large-scale simulations in 2D space. The work also deals with merging and unification of the 2D and 3D simulation using modern C++. A realistic example of use is ultrasound simulation in transcranial neuromodulation and neurostimulation in large domains, which have more than 16384x16384 grid points. Simulation of such size may take several days if we use the original MATLAB 2D k-Wave. Speedup of the new implementation is up to 8 on the Anselm and Salomon supercomputers.

Simulácia šírenia ultrazvuku prostredníctvom mäkkých biologických tkanív má širokú škálu praktických aplikácií. Patria sem dizajn prevodníkov pre diagnostický a terapeutický ultrazvuk, vývoj nových metód spracovania signálov a zobrazovacích techník, štúdium anomálií ultrazvukových lúčov v heterogénnych médiách, ultrazvuková klasifikácia tkanív, učenie rádiológov používať ultrazvukové zariadenia a interpretáciu ultrazvukových obrazov, modelové vrstvenie medicínskeho obrazu a plánovanie liečby pre ultrazvuk s vysokou intenzitou. Ultrazvuková simulácia však predstavuje výpočtovo zložitý problém, pretože simulačné domény sú veľmi veľké v porovnaní s akustickými vlnovými dĺžkami, ktoré sú predmetom záujmu. Ale ak je problém osovo symetrický, problém môže byť riešený v 2D.To umožňuje spúšťanie simulácií na mriežke s väčším počtom bodov, s menším využitím výpoč- tových zdrojov za kratšiu dobu. Táto práca modeluje a implementuje zrýchlenie vlnovej nelineárnej ultrazvukovej simulácie v axisymetrickom súradnicovom systéme realizovanom v Matlabe pomocou Mex súborov pre diskrétne sínové a kosínové transformácie. Axisymetrická simulácia bola implementovaná v C++ ako open source rozšírenie K-WAVE toolboxu. Kód je optimalizovaný na beh na jednom uzle superpočítaču Salomon (IT4Innovations, Ostrava, Česká republika) s dvoma dvanásť-jadrovými procesormi Intel Xeon E5-2680v3. Na maximalizáciu výpočtovej efektívnosti boli vykonané viaceré optimalizácie kódu. Po prvé, fourierové tramsformácie boli vypočítané pomocou real-to-complex FFT z knižnice FFTW. V porovnaní s complex-to-complex FFT to znížilo čas výpočtu a pamäť spojenú s výpočtom FFT o takmer 50%. Taktiež diskrétne sínové a kosínové transformácie sa počítali pomocou knižnice FFTW, ktoré v Matlab verzii museli byť vyvolané z dynamicky načítaných MEX súborov. Po druhé, aby sa znížilo zaťaženie priepustnosti pamäte, boli všetky operácie počítané jednoduchej presnosti pohyblivej rádovej čiarky. Po tretie, elementárne operá- cie boli paralelizované pomocou OpenMP a potom vektorizované pomocou rozšírení SIMD (SSE). Celkový výpočet C++ verzie je až do 34-násobne rýchlejší a využíva menej ako tretinu pamäte ako Matlab verzia simulácie. Simulácia ktorá by trvala takmer dva dni tak môže byť vypočítaná za jeden a pol hodinu. Toto všetko umožňuje počítať simuláciu na výpočetnej mriežke s veľkosťou 16384 × 8192 bodov v primeranom čase.

This thesis is a part of the k-Wave project, which is a toolbox for the simulation and reconstruction of acoustic wave felds and one of its main contributions is the planning of focused ultrasound surgeries (HIFU). One simulation can take tens of hours and about 60% of the simulation time is taken by the calculation of the 3D Fast Fourier transforms. Up until now the 3D FFT has been calculated purely by the FFTW library and its 1D decomposition, whose major limitation is the maximum number of employable cores. Therefore we introduce a new approach, called the 2D hybrid decomposition of the 3D FFT (HybridFFT), where we combine both MPI processes and OpenMP threads to reach as best performance as possible. On a low number of cores, on the order of a few hundreds, we are about as fast or slightly faster than FFTW and pure MPI 2D decomposition libraries (PFFT and P3DFFT). One of the best results was achieved on a 512^3FFT using 512 cores, where our hybrid version run 31ms, FFTW run 39ms and PFFT run 44ms. The most significant performance advantage should be seen when employing around 8-16 thousand cores, however we haven't had an access to a machine with such resources. Almost a linear scalability has been proven for up to 2048 employed cores.

The main focus of this project is usage of multi - GPU systems and usage of CUDA unified memory . Its goal is to accelerate computation of 2D and 3D FFT, which is the main part of simulations in k- Wave library .K- Wave is a C++/ Matlab library used for simulations of propagation of ultrasonic waves in 1D , 2D or 3D space . Acceleration of these functions is necessary , because the simulations are computationally intensive .

This document introduces a brand new method of the 1D, 2D and 3D decomposition with the use of local Fourier basis, its implementation and comparison with the currently used global 1D domain decomposition. The new method was designed, implemented and tested primarily for future use in the simulation software called The k-Wave toolbox, but it can be applied in many other spectral methods. Compared to the global 1D domain decomposition, the Local Fourier decomposition is up to 3 times faster and more efficient thanks to lower inter-process communication, however it is a little inaccurate. The final part of the thesis discusses the limitations of the new method and also introduces best practices to use 3D Local Fourier decomposition to achieve both more speed and accuracy.

The main goal of this thesis is to describe the implementation of continuous integration into the k-Wave project. The thesis focuses primarily on the version written in the C/C++ language with the usage of the OpenMP library which typically runs on supercomputers. Accordingly, many of popular workflows and approaches ought to be adapted, a few more created. The outcome of the thesis is a complete solution with real and practical usage. The author provides design, tools selection, runtime environment administration and configuration for each one of the used services. Software implementation of the basic framework is used in order to utilize running tests on the supercomputers. Furthermore, the implementation of chosen types of regression and unit tests are performed. Realisation is based on Gitlab and Jenkis services that are running on separated Docker containers.