Full-wave simulation of large-scale wave fields - CSC

Full-wave simulation of large-scalewave fieldsTomi Huttunen, Timo LähivaaraInverse Problems GroupAki PulkkinenBiomedical Ultrasound GroupDepartment of PhysicsUniversity of KuopioFull-wave simulation of large-scale wave fields – p. 1

Outline of the talk• Background of the study• Challenges in the modeling of waves• Discontinuous Galerkin methods for waveproblems (Ph.D. project of Timo Lähivaara)• Modeling of optoacoustic imaging (MasterThesis of Aki Pulkkinen)Full-wave simulation of large-scale wave fields – p. 2

Background, a short history• The development of simulation tools started1999.• The application was Focused Ultrasound surgery(an Academy funded project)• A parallel UWVF code for acoustics (2003).• Time domain methods, Timo’s project (2006)• Waveller IPRs currently at spin-off companyKuava Oy (founded 2007)• Waveller used here as a reference solver.Full-wave simulation of large-scale wave fields – p. 3

Problems with waves• “A rule of thumb” for low-order FEM and FDMis ten points per wavelength λ• Due to the numerical pollution, even densermeshes are needed at high frequencies• Boundary element methods (BEM) becomecomplex for problems in inhomogeneous media• Ray-approximations are commonly used ⇒reduced accuracyFull-wave simulation of large-scale wave fields – p. 4

Consequently...• Clearly, we can consider that this problem[scattering of radar waves by an aircraft]remains unsolved and a completely new methodof approximation is needed to deal with the veryshort-wave solutionO.C. Zienkiewicz: “Achievements and someunsolved problems of the finite element method”.International Journal for Numerical Methodsin Engineering, 47, 9-28 (2000)• Special techniques are needed for themodeling of wavesFull-wave simulation of large-scale wave fields – p. 5

Discontinuous Galerkin methods (DGM)• The DGM use standard finite elements for spatial discretization• The basis is discontinuous but the continuity of the solution is enforcedover each element interface using physical transmission conditions(=numerical flux)• DGM results in a favorable matrix structure (block diagonal mass matrixetc.) and are easy to parallelize.• In the DGM weak formulation, one can also assume that the test andbasis functions are solutions of the local wave equation (e.g. plane waves)⇒ The ultra weak variational formulation (codes using UWVF: Wavellerand Comsol)Full-wave simulation of large-scale wave fields – p. 6

DGMs of this project• Parallel, time-domain DGM for acoustics andelastic waves (Timo’s Ph.D. project)• Focus on the choice of the optimal polynomialbasis.• Waveller (frequency domain solver) used for thecomparison.• Evaluation of the parallel UWVF for largeelectromagnetic wave problems (modelproblems, for example, from Nokia).Full-wave simulation of large-scale wave fields – p. 7

DGM implementation• Time-domain DG codes are coded using C++ andMPI for parallelization.• Mesh partitioning using METIS so that load isevenly distributed between processors.• Electromagnetic UWVF is a Fortran90+MPIcode.• Commercial tools for meshing (Gambit, Comsol,...)Full-wave simulation of large-scale wave fields – p. 8

Acoustic model problemSound from a loudspeaker.Full-wave simulation of large-scale wave fields – p. 9

Near-fieldSimulated near field at 1000 Hz.Full-wave simulation of large-scale wave fields – p. 10

Far-field120UWVFDGmeasurementxz plane90160120yz plane901601500.5301500.530180 0180 0210330210330240270300240270300Comparison with measurements.Full-wave simulation of large-scale wave fields – p. 11

Axial response10.510.8UWVFDGmeasurementAmplitude0−0.5Amplitude0.60.40.2−10 2 4t (ms)601000 1500 2000 2500 3000f (Hz)Comparison with measurements.Full-wave simulation of large-scale wave fields – p. 12

Elastic wavesScattering of a plane wave from a bar.Full-wave simulation of large-scale wave fields – p. 13

Electromagnetic scatteringz (m)−2 024100y (m)−10−100x (m)10Model geometryFull-wave simulation of large-scale wave fields – p. 14

Electromagnetic scatteringScattering of EM waves from a full-size aircraft at 0.3GHz.Full-wave simulation of large-scale wave fields – p. 15

DGM, conclusions• Time-stepping is a challenge for time-domainproblems (high order polynomial basis requiressmall time steps)• Local time stepping might help but may bedifficult to parallelize.• The UWVF method scales well and is suitable forlarge problems.• The challenges for the UWVF are extremelysmall geometric details of the model (or lowfrequencies) and singular fields.Full-wave simulation of large-scale wave fields – p. 16

Optoacoustic imaging (OAI)• A short laser pulse (10 ns-100µs) is targeted to atissue• The absorption of the light leads to pressure pulsewhich propagates as ultrasound• Measurement of optoacoustically generatedsound provides information of the optical andacoustical properties of the medium.• The aim was study the feasibility of the methodfor transcranial imaging of veins.Full-wave simulation of large-scale wave fields – p. 17

Why OAI? Pros and Cons• The aim is to combine best features of optical andultrasonic imaging.• Large diffence is optical properties of tissues ⇒strong contrast• Good spatial resolution of ultrasound.• However, the method suffers from small imagingdepth and weak acoustic signals.Full-wave simulation of large-scale wave fields – p. 18

Model for Optoacoustic imaging• A Monte Carlo model for the propagation oflight.• Linear inhomogeneous wave equation forultrasound (solved using FDTD).• The simulation medium consists of a head andbrain of mouse(B. Dogdas, D. Stout, A. Chatziioannou, and R.M. Leahy, "Digimouse: A 3D Whole BodyMouse Atlas from CT and Cryosection Data."Phys Med Biol. 2007 Feb 7; 52 (3): 577-87).• The imaging target is blood oxygen saturation.Full-wave simulation of large-scale wave fields – p. 19

Geometry of the modelUS transducer on the left, mouse head on the right.Full-wave simulation of large-scale wave fields – p. 20

Optical absorptionLogarithmic optical absorption in the mouse head.Full-wave simulation of large-scale wave fields – p. 21

Acoustic pressureMaximum pressure amplitude in the mouse head.Full-wave simulation of large-scale wave fields – p. 22

Measured signal600Acoustical pressure as measured by the focusing transducerWithout veinSO 2= 100%SO 2= 0%500400300p (Pa)2001000−100−20015 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20t (µ s)Measured signal at the transducer.Full-wave simulation of large-scale wave fields – p. 23

OAI, conclusion• The work provided valuable information foroptimization of the imaging parameters.• The method still suffers from the weak acousticsignal due to strong absorption in the skull.• Aki’s work continues at Sunnybrook SciencesCentre (University of Toronto, Canada).Full-wave simulation of large-scale wave fields – p. 24

Summary of results• The grant gave a unique opportunity for twostudents to perform simulations on the bestimaginable computer (fast generation of data).• Two journal papers Timo’s Ph.D. thesis (onesubmitted to IJNME and another in preparation)+ several conference talks• Aki’s MS. thesis + continuation resultsFull-wave simulation of large-scale wave fields – p. 25