Fast and Accurate Multiscale Electromagnetic Modeling Framework: An Overview

Transcription

1 Fast and Accurate Multiscale Electromagnetic Modeling Framework: An Overview W.C. Chew, A.C. Cangellaris, J. Schutt-Ainé Dept. Elec. Comp. Engg. U of Illinois Urbana-Champaign Urbana, IL 61801, USA w-chew@uiuc.edu H. Braunisch, Z.G. Qian, A.A. Aydiner, K. Aygün Intel Corporation Chandler, AZ 85226, USA henning.braunisch@intel.com L.J. Jiang, Z.H. Ma, L.L. Meng, M. Naeem Dept. Elec. Electronic Engg. The U of Hong Kong Hong Kong SAR, China jiangjl@eee.hku.hk

2 Outline Introduction; Past works in the area; Multiscale problems; Augmented electric field integral equation (A- EFIE); A-EFIE for layered media; The power of encapsulation; Equivalence principle algorithm; A-EPA and A-EFIE; When can we outdo commercial software? Conclusions 2 2

3 Multi-Scale Multi-Physics Phenomena in CEM Disparate sizes in geometrical models induces both low-frequency circuit physics and highfrequency wave physics, giving rise to computational challenges. Chip Package Chassis 5/18/2013 3

4 Dept. of Electrical and Electronic Engineering The University of Hong Kong MULTISCALE TO MULTIPHYSICS With the increasing scales, the dominant physics also changes. W.C. Chew and L.J. Jiang, Overview of Large Scale Computing: Past, Present, and Future, the Proceedings of IEEE, vol. 101, no. 2, pp , Feb L.J. Jiang

5 Intro: The Tale of Three Physics Circuit Physics Wave Physics Ray Physics W.C. Chew, Computational Electromagnetics---the Physics of Smooth versus Oscillatory Fields, Philo. Trans. Royal Soc. London Series A, Math., Phys. Eng. Sci. Theme Issue Short Wave Scattering, vol. 362, no. 1816, pp , March 15, Yagi-Uda

6 Center of Charge Method (CCM) for Laplace s Equation Circuit Physics First Order Second Order L. J. Jiang, and W. C. Chew, "A New Capacitance Extraction Method", J. Electromag. Waves Appl., vol. 18, no. 3, pp , 2004.

7 Multiple-Reflections in the Multilayer Green s Function (Laplace Problem) Outgoing to local multipole translator Closed form of the outgoing to local multipole translator Y. C. Pan and W. C. Chew, A fast multipole method for embedded structure in a stratified medium, J. Electromagn. Waves Appl.,Vol. 18,No. 2, pp , 2004.

8 DCIM Speedup Signal Lines and Vias (Laplace Problem) L. J. Jiang, W. C. Chew, and Y. C. Pan, Capacitance Extraction in the Multilayer Medium Using DCIM and SMFMA, J. of Electromag. Waves and Appl.. vol. 19. No. 14, , 2005.

9 Low-Frequency--Formulations Twilight Zone Decoupling of Electric and Magnetic Fields at DC The Maxwell s equations can be written as follows when the frequency is right at zero E 0, E lim J/ i H J, H 0 0 It is easy to see that the electric and magnetic fields are decoupled at DC and the current can be decomposed as J J J sol irr divergence-free curl-free H E

10 Low Frequency--Formulations Inductance Physics Loop Basis: divergence free Capacitance Physics Star Basis: quasi-curl-free. Tree Basis: RWG basis with the basis along a cut removed. The cut prevents the rest of the RWG basis (tree basis) from forming any loop. LS or LT formulation isolates the contribution of vector potential and scalar potential. Information of vector potential will not be lost due to machine precision.

11 Hertzian Dipole from Zero to Microwave Frequencies (JS Zhao) Input admittance/impedance of a Hertzian dipole at very low frequencies and at higher frequencies J. S. Zhao, W. C. Chew, Integral Equation Solution of Maxwell's Equations from Zero Frequency to Microwave Frequencies, IEEE Trans. Antennas Propagat., James R. Wait Memorial Special Issue, vol. 48. no. 10, pp , Oct (Schekulnoff Best Paper)

12 EVANESCENT AND PROPAGATING WAVES Two different kernels Static Source. e.g. charges G 1 r dg dr 1 2 r 2 r 6 r 2 dg 2 3 dr 3 dg 3 4 dr 1 O 2, r 1 O 3, r 1 O 4, r r r r Dynamic Source. e.g. Hertian dipole G ikr e r dg e ~ ik dr r ikr 2 ikr dg ~ 2 e k 2 dr r 3 ikr dg ~ 3 e ik 3 dr r 1 O, r 1 O, r 1 O, r r r r

13 Acceleration Technique: Multilevel Fast Multipole Algorithm (MLFMA, Dynamic/Wave Physics) The final computational complexity of the algorithm is O(N log N). The matrix A is never generated, but only the smaller diagonal matrices and T (translators): A matrix-free method. The translators use multipoles as basis functions for low frequency, but use plane waves as basis functions for wave physics. Coifman, Rokhlin, Wandzura, 1993, Rokhlin & Greengard, Laplace Solver,1987. Song, Lu, and Chew, EM Wave Solver, 1995, 1996, N log N algorithm.

14 Mixed Form Fast Multipole Algorithm--MF-FMA (Non-Diagonal to Diagonal Translation) w/ L.J. Jiang Circuit Physics Wave Physics Circuit Physics L.J. Jiang and W.C. Chew, A mixed form fast 14

15 Grr (, ', ) A-EFIE Formulation, and LF and Broadband Scheme Electric field integral equation (EFIE) Most popular w/ LF breakdown ikr e I 2 k 4 R Augmented EFIE [1] KVL KCL ik T 1 V D P 0 0 b 2 k c D 0 U 0ρ 0 T S D P D P D D J ik c ρ 0 0 Charge neutrality: 0 ik0 0V S J b ik0 Patch-based scalar potential matrix Incidence matrix of graph G J n 0 n KVL and KCL Voltage excitation graph G Z. G. Qian and W. C. Chew, Microwave and Optical Technology Letters, vol. 50, no. 10, pp , Oct Z.-G. Qian, and W.C. Chew, IEEE Trans. Antennas and Propagat., vol. 57, no. 11, pp , Nov

16 Example: Four-Layer Package Intel Collaboration All four layers whole board Almost all nets Mesh generator GUI Triangular Mesh Number of inner edges:

17 Example: Four-Layer Package Frequency: 1 GHz Total solving time: 98 min Seven-level FMA setup: 4.1 min Matrix filling: 33.5 min Preconditioner inverse: 17.4 sec GMRES(50) iteration : 60.5 min Average time per iteration: 27.1 sec Preconditioning time per iteration: 2.3 sec Total memory usage: 6.2 GB Preconditioner: 0.3 GB Testing machine: Single CPU 3.00 GHz Excitation Surface electric current density Unit : A/m, db scale Triangular Mesh Number of inner edges:

18 Movie of Current 1 GHz Multi-scale Package Solved with A-EFIE on a Single CPU 18

19 Movie of Current 3 GHz Multi-scale Package Solved with A-EFIE on a Single CPU 19

20 A-EFIE for Layered Medium Green s Function (Y.P. Chen) A-EFIE stable down to DC Y.P. Chen, L. Jiang, Z.-G. Qian, and W. C. Chew, "An augmented electric field integral equation for layered medium Green s function," IEEE Trans. Antennas Propagat., vol. 59, no. 3, pp , March, 2011.

21 The Power of Encapsulation Divide and defeat (DaD); Modularization; Object oriented concept; Encapsulate the solution in a black box, and have the black boxes interact with each other.

22 EPA for Multi-scale Problem EPA Equivalence Principle Algorithm Enclose fine features by the virtual equivalence surfaces Well conditioned problem among equivalence surfaces Reduction of the final matrix dimension Wave physics and circuit physics are separated Essentially a domain decomposition method Solve each domain independently Easy to hybridize with different methods Easy for parallelization (embarrassingly simple) W. C. Chew and C. C. Lu, The use of Huygens' equivalence principle for solving the volume integral equation of scattering, IEEE Trans. Ant. Propag., vol. AP-41, no. 7, pp , July M. K. Li and W. C. Chew, Micro. Opt. Tech. Lett., v. 48, no. 9, pp , Sept M. K. Li and W. C. Chew, IEEE Trans. Antenna Propag., vol. 55, no. 1, pp , Equivalence surface 22

23 EQUIVALENCE PRINCIPLE ALGORITHM Separates the whole solution domain into sub-domain based on their physical structures Separation of small and fine parts from large and smooth structures Decompose into circuit physics and wave physics

24 EQUIVALENCE PRINCIPLE ALGORITHM

25 Generalized Impedance Boundary Condition (GIBC) GIBC Operator A powerful way to characterize an arbitrary metallic/dielectric object; The GIBC operator can be found using FEM; GIBC allows complex inhomogeneity to be treated easily, including metallic objects, anisotropy, and magnetic materials; Volume integral equation can be used to find this operator as well: A general arbitrary inhomogeneous problem where each object is described by a generalized impedance boundary condition (GIBC) operator The GIBC operator from FEM, in this case is: S. Q He, W. E. I. Sha, L. J. Jiang, W. C. H. Choy, W. C. Chew, Z. P. Nie, Finite Element Based Generalized Impedance Boundary Condition for Modeling Plasmonic Nanostructures, IEEE Transactions on Nanotechnology, Published on line. DOI: /TNANO

26 EPA Application: XM Antenna on Ground Plane EPA turns an ill-conditioned problem into a well-conditioned one XM Antenna has 1926 triangles and 2192 tetrahedrons MOM Number of unknowns 9304 Condition number 2.3E7 EPA Number of unknowns 3948 Condition number

27 EPA Application: XM Antenna Array 30 x 30 array Unknown Number 7.2 million Unknowns in equation 0.86 million Total memory usage 12 GB 149 iterations to 2.0x10-2 Each iteration uses 36.9 seconds Total solving time: 272 minutes (setup time 147 minutes) Dell Precision 690 with Intel Xeon 3.00GHz CPU, 16 GB RAM, and Linux OS. Close-up E x E z 27 27

28 EPA Application: XM Antenna on Car Current distribution Unknowns in EPA equation Frequency = GHz An 8-level MLFMA is used GMRES(50) is used, error < 2.0x10-2 after 200 iterations 54.2 s for each iteration Total memory usage is 2.6 GB Dell Precision 670 with Intel Xeon 3.00 GHz CPU and 4 GB RAM with Linux OS. Antenna close-up Close-up with current Radiation pattern 28 28

29 CIRCUIT PHYSICS: LOW FREQUENCY BREAKDOWN OF EPA The EPA suffers low-frequency breakdown There might be two reasons: EFIE operator inside each cell box EPA interactions Or both

30 A-EPA WITH A-EFIE Outside: EFIE solver Inside: A-EFIE solver Augmented EPA method Plane wave incident Frequency: 5GHz

31 Ball Grid Array Model d d d d=2mm A EPA+A EFIE feed Current distribution at freq: 300MHz

32 When Can We Out Do Commercial Codes? Potential Distribution (AEFIE) Operating frequency = 1GHz Scheme type = MoM w FMA (5 layers, 4 harmonics) Error = E-02 Simulation time = secs

33 Current Distribution (HFSS) Operating frequency = 1GHz Simulation time = 7 hrs and 40 mins Delta mag. energy =

34 Structure w Plates (Geometry) PEC material No of unknowns = 2,823,625 Wee kly Rep ort Maji d Nae em

35 Current Distribution (AEFIE) Operating frequency = 1GHz Scheme type = MoM w FMA (8 Levels and 3 Harmonics) Error = Simulation time = 46 mins, 30 secs Wee kly Rep ort Maji d Nae em

36 29 Layers Stack

37 Fast Poisson Solver (Zuhui MA, 2011) () r () r r () r gxy (, ) r nˆ D ( r) nˆ D g( x, y) r r ( r) D / Solve the equation in two stages using fast tree solver to invert div and del operators; O(N) complexity is possible. 37

38 Hierarchical Loop Basis where 38

39 Jose Schutt-Aine LIM-Spice Simulations No. of Nodes SPICE (sec) 70,000 70,000 70,000 70,000 70, time = 20 time = 60 time = 120 time = 160 time = 200 Parsing < Simulation Total LIM SPICE Parsing < (sec) Simulation Total Speedup Total/Total

40 Jose Schutt-Aine Improved TL Simulator 0 ImagS12 (with delay extracted) 0 ImagS12 (with delay extracted) Approximated Approximated Original Original S S Frequency (GHz) TL - Near End OLD METHOD VF METHOD Frequency (GHz) TL - Far End OLD METHOD VF METHOD Volts Volts Time (ns) Time (ns) 40 40

41 Electro-Thermal Analysis Jose Schutt-Aine Cross section of the 3D structure (center cut) Comparison between two pictures from different tools Looking for correct temperature range and general distribution (color maps used by the tools are not exactly the same) In general, very good correlation is observed

42 Model Size Issues Jose Schutt-Aine Mesh density considerations coarse mesh results in errors in heat flux calculation geometry of the structure structure of the underlying PDN sizes of elements of interest (TSVs, solder balls, etc.) # 1 # 2 # Elements Run time LIM (C++) Run time LIM (MATLAB) Run time HSPICE , (total) 2 3,514, (total) Typically the size of the equivalent circuit is very large Traditional solvers (SPICE) do not scale well with the size of the model

43 EFFECTIVE MASS APPROXIMATION Quantum device with three semi-infinite leads. J. Huang

44 QUANTUM BALLISTIC TRANSPORT For each incident wave from the leads Self-consistency is achieved Landauer Büttiker formula

45 Simulation Results 2D DGFET Jun Z. Huang, W. C. Chew, M. Tang, and L.J. Jiang, IEEE Trans. Electron Devices, vol. 59, no. 2, pp , Feb

46 Fast Evaluation of Self-Energy Matrices in Atomistic Modeling of Electron Transport Systems (Jun HUANG, 2012) 46

47 Conclusions We reviewed the morphing physics of electromagnetics from statics to optics; We present our past efforts in solving the circuit/chip problems; Recent attempts have been to use divide and defeat (DaD) scheme, and encapsulate the smaller solutions in black boxes; This will eventually allow us to piece together FIELD solutions for large and complex problems; Commercial software cannot tackle some problems we can; Review some work of colleagues.

48 Thank You for Listening!