Implementation of Source Concept in Matlab Miloslav Capek - PowerPoint PPT Presentation

Implementation of Source Concept in Matlab Miloslav ˇ Capek Department of Electromagnetic Field CTU in Prague, Czech Republic miloslav.capek@fel.cvut.cz Seminar at KTH Stockholm, Sweden January 19, 2017 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 1 / 31

Outline 1 Source Concept 2 Yet Another Challenge 3 Method of Moments 4 AToM 5 AToM Architecture 6 Useful Tools to Know 7 Conclusion In this talk: ◮ for the first talk in the series proceed to capek.elmag.org , ◮ elementary knowledge in Matlab is expected, ◮ be extremely careful when comparing different sources (papers): different notation! . ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 2 / 31

Source Concept Source Concept Perspective topol- ogy and geometry Source concept. . . HPC, Modal de- algorithm ◮ represents a radiator(s) compositions efficiency completely by source currents J and M , Source Concept ◮ infers all parameters from a source current, i.e. L ( J , M ). Heuristic Integral and or convex variational optimization methods Sketch of main fields of the source concept. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 3 / 31

Source Concept What operators we know? ◮ assume operators in their matrix forms, i.e. , L → L ⇒ J → I • as far as meaningful, all algebraic operations are explicitly executable Impedance op. P r + 2j ω ( W m − W e ) → 1 2 I H ZI ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 4 / 31

Source Concept What operators we know? ◮ assume operators in their matrix forms, i.e. , L → L ⇒ J → I • as far as meaningful, all algebraic operations are explicitly executable Impedance op. P r + 2j ω ( W m − W e ) → 1 2 I H ZI Stored energy op. ( ka < 1) W sto → 1 4 I H ∂ X ∂ω I = 1 4 I H X ′ I ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 4 / 31

Source Concept What operators we know? ◮ assume operators in their matrix forms, i.e. , L → L ⇒ J → I • as far as meaningful, all algebraic operations are explicitly executable Impedance op. P r + 2j ω ( W m − W e ) → 1 2 I H ZI Stored energy op. ( ka < 1) W sto → 1 4 I H ∂ X ∂ω I = 1 4 I H X ′ I Far-field op. F ι ( r ) → F ι ( r ) I Near-field op. E ( r ) → N e ( r ) I , H ( r ) = N m ( r ) I Directivity op. D ι ( r ) → 4 π I H F H = I H U ι ( r ) I ι ( r ) F ι ( r ) I Z 0 I H RI I H RI ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 4 / 31

Source Concept What operators we know? ◮ assume operators in their matrix forms, i.e. , L → L ⇒ J → I • as far as meaningful, all algebraic operations are explicitly executable Impedance op. P r + 2j ω ( W m − W e ) → 1 2 I H ZI Stored energy op. ( ka < 1) W sto → 1 4 I H ∂ X ∂ω I = 1 4 I H X ′ I Far-field op. F ι ( r ) → F ι ( r ) I Near-field op. E ( r ) → N e ( r ) I , H ( r ) = N m ( r ) I Directivity op. D ι ( r ) → 4 π I H F H = I H U ι ( r ) I ι ( r ) F ι ( r ) I Z 0 I H RI I H RI Resistance op. P L → 1 2 I H ΣI Electric moment op. p → PI Magnetic moment op. m → MI ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 4 / 31

Source Concept What are Operators Good For? W W J 1 J 2 1. Determine lower/upper bounds, W B W A 2. estimate optimal trade-offs between various parameters, J ( r A ) J ( r B ) 3. find proper feeding networks, W max 4. understand underlying physics, W 0 W final 5. try to make material synthesis, W max 6. try to modify shape of source region. VG 2A VG 2B VG 1 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 5 / 31

Source Concept Example: Characteristic Modes of PEC Fractal Plate XI u = λ u RI u IFS fractal, 2nd iteration, PEC, ka = 0 . 5. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 6 / 31

Source Concept Example: Characteristic Modes of PEC Fractal Plate XI u = λ u RI u Current density J 1 of the first characteristic mode. Radiation pattern for the first characteristic mode. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 6 / 31

Source Concept Example: Spatial Decomposition of U-notched antenna 1 1 � � � � � R 11 R 12 I 1 I H RI = � I H I H 1 2 R 21 R 22 I 2 2 2 3 J 1 È J 2 J 1 J 2 2 1 P r [W] 0 ( J 1 È J 2 , J 1 È J 2 ) entire antenna P r arms only P r ( J 1 , J 1 ) -1 meanders only P r ( J 2 , J 2 ) cross-terms 2 P r ( J 1 , J 2 ) -2 0.6 0.8 1 1.2 1.4 ka Spatial (structural) decomposition of double U-notched antenna. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 7 / 31

W Yet Another Challenge Feeding Synthesis ◮ optimal currents are not compatible with realistic feeding • check that V = ZI opt is dense vector full of non-zero entries ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 8 / 31

W Yet Another Challenge Feeding Synthesis ◮ optimal currents are not compatible with realistic feeding • check that V = ZI opt is dense vector full of non-zero entries ◮ structure needs to be modified • currents sub-optimal to I opt • heuristic optimization needed ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 8 / 31

Yet Another Challenge Feeding Synthesis ◮ optimal currents are not compatible with realistic feeding • check that V = ZI opt is dense vector full of non-zero entries ◮ structure needs to be modified • currents sub-optimal to I opt • heuristic optimization needed ◮ shape modification resembles NP-hard problem How much DOF we have? W N (unknowns) 28 52 120 ∞ possibilities unique solutions Complexity of geometrical optimization for given voltage gap (red line) and N unknowns. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 8 / 31

Yet Another Challenge Feeding Synthesis ◮ optimal currents are not compatible with realistic feeding • check that V = ZI opt is dense vector full of non-zero entries ◮ structure needs to be modified • currents sub-optimal to I opt • heuristic optimization needed ◮ shape modification resembles NP-hard problem How much DOF we have? W N (unknowns) 28 52 120 ∞ 5 . 24 · 10 29 1 . 39 · 10 68 1 . 15 · 10 199 possibilities ∞ 2 . 68 · 10 8 4 . 50 · 10 15 1 . 33 · 10 36 unique solutions ∞ Complexity of geometrical optimization for given voltage gap (red line) and N unknowns. ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 8 / 31

Yet Another Challenge Pixeling with Heuristic Optimization Example: Shape optimization (pixeling) with ad hoc specified feeding placement, PEC plate L × L/ 2, ka = 0 . 3. Antenna synthesis – how far can we go? ◮ On the present, only the heuristic optimization 1 . . . 1 Y. Rahmat-Samii and E. Michielssen, Eds., Electromagnetic optimization by genetic algorithm . Wiley, 1999 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 9 / 31

Yet Another Challenge Pixeling with Heuristic Optimization Example: Shape optimization (pixeling) with ad hoc specified feeding placement, PEC plate L × L/ 2, ka = 0 . 3. Antenna synthesis – how far can we go? ◮ On the present, only the heuristic optimization 1 . . . Computational time: 12116 s Result of heuristic structural optimization using MOGA NSGAII from AToM-FOPS. 1 Y. Rahmat-Samii and E. Michielssen, Eds., Electromagnetic optimization by genetic algorithm . Wiley, 1999 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 9 / 31

Yet Another Challenge Pixeling with Heuristic Optimization Example: Shape optimization (pixeling) with ad hoc specified feeding placement, PEC plate L × L/ 2, ka = 0 . 3. Antenna synthesis – how far can we go? ◮ On the present, only the heuristic optimization 1 . . . Computational time: 1155 s Computational time: 12116 s Result of deterministic in-house algorithm removing in Result of heuristic structural optimization using MOGA each iteration the “worse” edge. NSGAII from AToM-FOPS. 1 Y. Rahmat-Samii and E. Michielssen, Eds., Electromagnetic optimization by genetic algorithm . Wiley, 1999 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 9 / 31

Yet Another Challenge Pixeling with Heuristic Optimization Example: Shape optimization (pixeling) with ad hoc specified feeding placement, PEC plate L × L/ 2, ka = 0 . 3. Antenna synthesis – how far can we go? ◮ On the present, only the heuristic optimization 1 . . . Q ( I ) /Q TM Q ( I ) /Q TM Chu = 7 . 23 Chu = 7 . 24 Resulting sub-optimal current approaching minimal Resulting current given by in-house deterministic value of quality factor Q . algorithm. 1 Y. Rahmat-Samii and E. Michielssen, Eds., Electromagnetic optimization by genetic algorithm . Wiley, 1999 ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 9 / 31

× × × × × × × Yet Another Challenge Structure of Solution Space 2 ◮ all combinations for N = 28 edges (5 . 24 · 10 29 ) calculated in Matlab • 3 days on supercomputer, 2 resulting vectors + permutation table ≈ 55 GB 2 Work still in progress. For recent updates visit EuCAP 2017 presentation Excitation of Optimal and Suboptimal Currents . ˇ Capek, M., CTU in Prague Implementation of Source Concept in Matlab 10 / 31