openems afreeandopenelectromagneticsolver Jan Taro Svejda, Thorsten Liebig, Andre Rennings, Daniel Erni

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1 openems afreeandopenelectromagneticsolver Jan Taro Svejda, Thorsten Liebig, Andre Rennings, Daniel Erni General and Theoretical Electrical Engineering (ATE) University of Duisburg-Essen, Duisburg, Germany April 17, 2014 Outline 1 Introduction 2 EC FDTD in openems 3 openems workflow 4 Show case: Head loop coil 5 Further show cases 6 Conclusion & Outlook Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 2 / 28

2 What is openems? OpenEMS ia an opensource 3D electromagnetic field solver Calculations are based on the EC FDTD scheme 1 Problems can be solved in cartesian coordinates or cylindrical coordinates Controlled by the powerfull and easy to use Matlab/Octave scripting interface Postprocessing directly in Matlab/Octave Field plots in Matlab/Octave or with the free tool Paraview Suitable for Linux and Windows platforms 1 equivalent circuit (EC) finite-diference time-domain (FDTD) Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 4 / 28 Advantages of the EC FDTD scheme The EC FDTD and conventional FDTD scheme are numerically equivalent with all the corresponding (dis)advantages of the FDTD method Time domain method broadband solution with one simulation Resources scale linearly with problem size Easy integration of advanced dispersive material models (e.g. multi polar Drude/Lorenz) All known advanced FDTD features (e.g. PML boundary contitions) can be used in the EC FDTD scheme Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 6 / 28

3 Cartesian EC-FDTD Mesh The cartesian EC-FDTD mesh consists of rectangular boxes Primary mesh lines for E field (red) Displaced mesh lines for H field (blue) Yee cell scheme E r (n z + 1) A y E z H x H y E x (n z + 1) Ñ E z (n x + 1) A α E z H r H α E z (n r + 1) N E y H z E x H z (n y 1) H y (n z 1) (a) cartesian E α H z E r H z (n r 1) H α (n z 1) (b) cylindrical Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 7 / 28 Cylindrical EC-FDTD mesh Different stages of mesh complexity possible: primary mesh dual mesh primary mesh dual mesh primary mesh dual mesh r α α r α (a) partial cylindrical mesh (b) closed α mesh (c) full cylindrical mesh Some special treatments are necessary: Closed α mesh: A special boundary condition in ±α direction is needed Full cylindrical mesh: A special EC-FDTD operator at r = 0 is necessary Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 8 / 28

4 Drawback of a full cylindrical mesh α α Very tiny cells around the center (r = 0) Very small time step and very long simulation time Solution: Using sub-grids with reduced α resolution Much larger time step and shorter simulation time Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 9 / 28 openems workflow 1 Create a new simulation script (Matlab/Octave) Include physical constants Set parameters for the problem Setup materials Initialize FDTD (gaussian puls) Define boundary conditions Setup structure with geometric primitives Add ports Create the mesh (most important step!) Define dump boxes 2 View and controll the geometry and mesh (AppCSXCAD) 3 Run the simulation 4 Do Postprocessing with Matlab/Octave or Paraview Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 11 / 28

5 The simulation setup Problem in cartesian coordinates Coil includes metal strips (blue), lumped capacitors (red) and one lumped port (red) Resonance frequency at 300 MHz Placed near a head phantom with four materials Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 13 / 28 Simulation results I Loop coil reflection coefficient S 11 and input admittance Y 11 displayed with Matlab real imag reflection coefficient S 11 (db) admittance Y in (S) frequency f / MHz (a) reflection coefficient (with Z ref = 10Ω) frequency f (MHz) (b) feed port admittance Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 14 / 28

6 Simulation results II SAR and B ± 1 field distributions of the loop coil displayed with Matlab (c) SAR (linear) (d) B + 1 (log10) (e) B 1 (log10) Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 15 / 28 Simulation results III 3D view of the SAR distribution shown with Paraview Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 16 / 28

7 Feature circuit simulatior OpenEMS can use a built in circuit simulator for advanced field superpositions Example of the head loop coil: All capacitors are replaced by lumped ports Run simulations for each port (coil is now not resonant) Connect a network at each port (e.g. just the capacitors) Calculate complex coefficients with the currents flowing into the ports Superpose the fields of each port with the complex coefficients Optimize the capacitor values easily wihtout new simulations Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 17 / 28 6channelheadloopcoilI Problem in cylindrical coordinates Virtual family model used Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 18 / 28

8 6channelheadloopcoilII Normalized local SAR for each individual coil: Jan Taro Svejda EDUHF LAB MRI 2014 in Magdeburg, Germany 19 / 28 6channelheadloopcoilIII Multi transmit local SAR examples: (a) V n = 1; n = 1..6 (b) V n = exp(j n 2π N ); n = 1..6 Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 20 / 28

9 Simple low pass birdcage Native fit to the cylindrical mesh coarse mesh Parameterized structure (Matlab/Octave script) Circuit simulator for capacitor (tuning) Virtual Family model included Meander coil transmit array Bended coil fits to the cylindrical mesh Parameterized structure (Matlab/Octave script) Complex field superpositions for RF shimming/multi transmit in Matlab

10 Conclusion I OpenEMS is an EC FDTD electromagnetic field solver Suported coordiante systems are cartesian cylindrical (with subgrid) spherical in a future release Dispersive material models (e.g. multi polar Drude/Lorenz) All (dis)advantages of FDTD scheme Easily controlled by scripts in Matlab/Octave Parameterized structures Postprocessing directly in Matlab/Octave Arbitrary optimisations possible Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 25 / 28 Conclusion II Circuit simulator feature included Lumped components replaced by ports unresonant structure Field superposition with complex coefficients Field and structure optimisation without simulation reruns OpenEMS is a free and opensource software Suitable for Linux and Windows platforms No shareware needed Scripting with Octave 3D view and field display with Paraview or Octave Put your hands on and help to create new features... Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 26 / 28

11 Further reading For further information 1 : openems Website: openems Forum: openems Development: GNU Octave: Paraview: Feel free to download, evaluate and contribute T. Liebig, A. Rennings, S. Held, and D. Erni, openems - A free and open source equivalent-circuit (EC) FDTD simulation platform supporting cylindrical coordinates suitable for the analysis of traveling wave MRI applications, Int. J. Numer. Model., Special Issue on Optimization, vol. 26, no. 6, pp , Nov./Dec Jan Taro Svejda jan.svejda@uni-due.de EDUHF LAB MRI 2014 in Magdeburg, Germany 27 / 28