ALGORITHMS FOR SIMULATION OF SOUND PROPAGATION IN COMPLEX

ALGORITHMS FOR SIMULATION OF SOUND PROPAGATION IN COMPLEX DISPERSIVE ENVIRONMENTS Marjan Sikora, FESB, Split

Introduction n n simulation of sound propagation in environments with geometricaly complex boundaries reflection and refraction would be treated equaly – propagation in environments with several materials/media, both homogenous and dispersive this paper would present the review of existing simulation methods in order to find the most suitable one for our purpose also it would outline the method for simulating the propagation of the sound in environments described above

Two groups of simulations n Numerical simulations ¨ FEM ¨ FDM ¨ BEM n Geometric simulations ¨ Virtual source method ¨ Ray tracing ¨ Beam tracing

Numerical simulations n n n FEM Divides environment in finite elements Calculates solution for wave equation system Simulation of ultrasound propagation for design of ultrasound transducers [PZFlex] Simulates ultrasound transducers and propagation in human tissue

Advantages and limitations n n advantage: takes all wave phenomena into account limitations: uses one-way aproximation of wave equation – problem with reflective environments ¨ works well only in 2 D ¨ efficiency decreases with frequency ¨

Geometrical simulations based on principles of geometric acoustics n several methods: n ¨ virtual source method ¨ ray trace method ¨ beam trace method

Virtual source method [CATT, HEAD 3 D] n advantages: accuracy – important for early reflections ¨ uses point detector – no alliasing ¨ n dissadvantages: big demands for computing power and storage ¨ computations increase exponentialy O(nr) with order of reflections and number of faces/polygons ¨ cannot implement refraction, diffraction and diffuse reflections ¨

Ray tracing [ULYSES, EASE, CATT] n advantages: efficiency, works well with high order reflections ¨ can implement refraction [UTSIM], and diffraction ¨ n dissadvantages: problems with ray detection – uses spherical detector ¨ missed rays due to small radius of detector ¨ alliased and inexisting rays – due to big detector ¨ n compromise: ¨ ¨ ¨ l – mean length of rays N – number of rays r – radius of spherical detector

Ray tracing problems with early reflections n also misses late reflections n often used combined with virtual source method for early reflections and statistical “tail” for late reflections [ULYSES, EASE, CATT] n

Beam tracing [Farina – RAMSETTE, Drumm, Funkhouser] n n n uses pyramidal beams for tracing beams cover complete space around source – spatial coherence uses spherical detector

Beam tracing n n n adaptive system [Drumm, Funkhouser] diffuse reflections [Farina, Drumm] diffraction [Funkhouser, Tsingos]

Beam tracing n n dispersive environments not simulated refraction also not taken into account but method can be sophisticated to take into account this phenomena this method is suitable because of: spatial cohherence (unlike VSM and RT) ¨ efficiency in complex environments with high order of reflections (unlike FEM) ¨

Beam tracing in complex dispersive environment n n the method has to be chosen for simulation of propagation in complex environmets simulation examples: ¨ propagation of ultrasound in human brain ¨ propagation of sound in environment with high temperature gradient ¨ propagation of ultrasound in sea and sea bottom ¨ propagation of ultrasound in geological research application

Beam tracing in complex dispersive environment n n n complex environmets cannot be desribed only by single media and reflective boundaries they should be defined by materials/volumes and dicontinuums/planes discontinuum cause reflection and refraction

Beam tracing in complex dispersive environment n n propagation in dispersive media is treated by stohatical method beams are longitudinaly divided in homogenous segments are than randomly assigned density value which is in between of max and min density for specific material refraction of beam segment is than calculated based on the assigned density

Beam tracing in complex dispersive environment n n in existing application [Farina, Drumm, Funkhouser] model is composed of polygons this simulations are designed for arhitectural acoustics – simple geometry in complex dispersive invironments models are more complex – they have curved, organic forms so models have to be in form of TIN – triangular networks

Conclusion n n n several methods for simulation of propagation of sound in complex dispersive environments have been explored the beam tracing method was chosen as suitable it had to be able simulate complex environments where sound propagates in several materials because of this the classical one media/reflective boundary scene was abandoned due to organic, complex forms, the polihedrons are composed of triangles rather than polygons in order to simulate nonhomogenous materials stohastical method was added to beam tracer

Future work n completed: detailed object oriented data structure have been developed in order to store data about environment and data about traced beams ¨ general algorithms for adaptive beam trace with triangular network polyhedrons ¨ n under development: ¨ n detailed algorithms for adaptive beam tracing in homogenous and dispersive media to be completed: implementation in object oriented programming environment (c++) ¨ checking the efficiency of algorithms and memory demands for specified data structures ¨ testing on real world examples and optimization ¨