從二面角RCS看FEKO MOM and PO 物理光學法計算整理

從二面角RCS看FEKO MOM and PO 物理光學法計算整理

一般FEKO的ＰＯ都被預設為一次反射.假使要多次反射需另外在假設“Use multiple reflections”.
下列這個問題是在探討
1. 假使面上是有夾90度角的兩個面，PO 必須被假設“Use multiple reflections”
◎UserManual上有：“the Number of reflections must be at least 2 to calculate the scattering from a dihedral and at least 3 for a trihedral.”計算二面角反射次數至少爲2，三面角反射次數至少要設爲3，以前沒仔細看啊，呵呵。
◎ Use multiple reflections: When this item is checked, multiple reflections are considered for the ray tracing. The number of reflections that must be considered is set in the Number of reflections dialog. This parameter determines the number of reflections to be taken into account for triangles with labels in the specified range. (For example, theNumber of reflections must be at least 2 to calculate the scattering from a dihedral and at least 3 for a trihedral.) Increasing the number of reflections that must be considered significantly increases computation time, and this should only be done based on physical considerations.
2. 附上結果跟執行時間(Triangles Information: 25008 )
MOM - 4.885hr (4Core-1.221hr) / RAM 10.406GByte (4Core-2.602 GByte)
MOM/MLFMM 1.856hr (4Core-0.464 hr) / RAM 342.084 MByte (4Core-85.521MByte)
MOM/PO (Use multiple reflections =10) 107.888hr (4Core-26.972hr)/ RAM 56.411 MByte (4Core-14.103MByte)
New！
Intel(R) Xeon(R) CPU           X5482  @ 3.20GHz , Number of parallel processes:    8 on    2 CPUs
max. triangles:MAXNDR   =    25938
MOM         0.601hr(36.06 min)
MOM+ MLFMM  0.208hr(12.48 min)
MOM+ PO_multiple_reflections_10  8.846hr(8 hr 50.76 min)
3. 在5度跟85度左右有一個很明顯的差異,這部分還請高人來解釋.
...<--這部分後來我取 Linear，就還好。不知是否有人有更好的看法。

怎ㄇ都無法把圖片上傳阿...搞了快30分鐘了呢?

是不是图片太大了?我贴图的时候点浏览后再点插入就行了。
第一帖好像有两处错误，MOM/MLFMM 应该是342.084 MByte，MOM/PO应该是56.411 MByte。

感謝已更正！

FEKO Result
取 db

取 Linner

三角片數量

  

MOM_Time_RAM

MOM_MLFMM_Time_RAM

PO_Mutil_10_Time_RAM

5度和85度的结果有差异我这么解释：
如果同样做一个减法运算，假设MOM是1000.1－1000＝0.1，由于PO计算存在误差，PO计算成1000.01－1000＝0.01，这样就导致最小值差了10dB。而这种误差在最大值（结果较大，不存在大数减大数的情况）时候不明显，在最小值（相减运算）时候会凸显。
但是由于最小值一般没有实际意义，可以认为对结果没有影响。

小编的报告非常详细，学习了。
有个问题不明白， 请指点：
我对PO计算二次反射步骤的理解是：
1）计算平面波照射情况下所有三角形面元的电流。
2）用每个三角形面元的电流作为激励再去照射其它面元，这一步也就是所谓的二次反射。由此得出的电流密度就是考虑了二次反射后的电流密度。
从计算量的角度看，第一步应该是O(N)量级，第二步应该是O(N*N)量级，照理说应该和MOM的O(N*N)差不多，时间上不至于差这么多啊。
我认为原因可能在于：
1）MOM是构建完整的耦合矩阵，然后直接一次计算完成。
2） PO是逐步计算的，不是一次求解N×N矩阵，而是1×N，2×N……N×N这样下去的。每次计算之后，有些数据会需要重新生成、传递，因此时间上长多了。
不知大家怎么想这个问题。

分析得有道理，值得注意的是，PO二次反射计算时间很长，但是内存占用并不多

我想PO在小反射角度误差较大的原因是因为没有考虑棱边的散射

這個是之前FEKO的一個學習檔，在論壇上有整個 PDF (可以於資料庫中找到)
關於這兩章圖片應該可以在更深入的討論，請各位大俠提供看法..

新的 RUNTIME
Intel(R) Xeon(R) CPU           X5482  @ 3.20GHz; GenuineIntel family 6 model 7 stepping 6 brand id 0
2 physical CPUs with a total of 8 processors found (multi-core CPUs with max. 4 cores per physical CPU)
Number of parallel processes:    8 on    2 CPUs
max. triangles:MAXNDR   =    25938
MOM         0.601hr(36.06 min)
MOM+ MLFMM  0.208hr(12.48 min)
MOM+ PO_multiple_reflections_10  8.846hr(8 hr 50.76 min)
                    SUMMARY OF REQUIRED TIMES IN SECONDS
                                            CPU-time      runtime
Reading and constructing the geometry         0.390        0.390
Checking the geometry                         0.219        0.219
Initialisation of the Greens function         0.000        0.000
Calcul. of coupling for PO/Fock               0.000        0.000
Calcul. of matrix elements                  383.359      383.359
Calcul. of right-hand side vector             1.032        1.028
Preconditioning system of linear eqns.       59.358       59.360
Solution of the system of linear eqns.     1717.345     1717.347
Determination of surface currents             0.000        0.000
Calcul. of impedances/powers/losses           0.091        0.092
Calcul. of averaged SAR values                0.000        0.000
Calcul. of power ideal receiving ant.         0.000        0.000
Calcul. of cable coupling                     0.000        0.000
Calcul. of electric near field                0.000        0.000
Calcul. of magnetic near field                0.000        0.000
Calcul. of far field                          0.375        0.375
                            other              0.237        0.236
                                         -----------  -----------
                         total times:       2162.406     2162.406
               (total times in hours:          0.601        0.601)
Specified CPU-times are referring to the master process only
Sum of the CPU-times of all processes:    17299.251 seconds (    4.805 hours)
On average per process:                    2162.406 seconds (    0.601 hours)
Peak memory usage during the whole solution:    1.413 GByte
(refers to the master process only)
Sum of the peak memory of all processes:       11.236 GByte
On average per process:                         1.405 GByte
MOM+ MLFMM  0.208hr(12.48 min)
                    SUMMARY OF REQUIRED TIMES IN SECONDS
                                            CPU-time      runtime
Reading and constructing the geometry         0.454        0.453
Checking the geometry                         0.203        0.203
Initialisation of the Greens function         0.000        0.000
Calcul. of coupling for PO/Fock               0.000        0.000
Calcul. of the FMM transfer function          0.500        0.500
Fourier transform of FMM basis funct.         0.250        0.250
Calcul. of matrix elements                   12.360       12.359
Calcul. of right-hand side vector             1.145        1.137
Preconditioning system of linear eqns.        7.297        7.297
Solution of the system of linear eqns.      720.079      720.087
Determination of surface currents             0.000        0.000
Calcul. of impedances/powers/losses           0.077        0.079
Calcul. of averaged SAR values                0.000        0.000
Calcul. of power ideal receiving ant.         0.000        0.000
Calcul. of cable coupling                     0.000        0.000
Calcul. of electric near field                0.000        0.000
Calcul. of magnetic near field                0.000        0.000
Calcul. of far field                          7.636        7.638
                            other              0.406        0.403
                                         -----------  -----------
                         total times:        750.407      750.406
               (total times in hours:          0.208        0.208)
Specified CPU-times are referring to the master process only
Sum of the CPU-times of all processes:     6003.250 seconds (    1.668 hours)
On average per process:                     750.406 seconds (    0.208 hours)
Peak memory usage during the whole solution:   62.039 MByte
(refers to the master process only)
Sum of the peak memory of all processes:      481.675 MByte
On average per process:                        60.209 MByte
MOM+ PO_multiple_reflections_10  8.846hr(8 hr 50.76 min)
  Physical Optics approximation or the Fock-theory is used for
  triangles with the following labels:
        Label                 PO/Fock  NOSHADE  MAXREF
              Cuboid1.Face1     PO        0         10
              Cuboid1.Face2     PO        0         10
  Meaning of NOSHADE:
   0 = Full ray tracing is performed, each side of the triangle
       can be illuminated.
   1 = No ray tracing, it is assumed that the triangle is directly
       illuminated by the sources and by the whole MoM region.
       The side is determined automatically.
   2 = Ray tracing is performed, however, the triangle can only
       be illuminated on the side from which the normal vector
       is pointing away, not on the back.
                    SUMMARY OF REQUIRED TIMES IN SECONDS
                                            CPU-time      runtime
Reading and constructing the geometry         0.453        0.453
Checking the geometry                         0.219        0.219
Initialisation of the Greens function         0.000        0.000
Calcul. of coupling for PO/Fock           31843.845    31843.846
Calcul. of matrix elements                    0.000        0.000
Calcul. of right-hand side vector             0.000        0.000
Preconditioning system of linear eqns.        0.000        0.000
Solution of the system of linear eqns.        0.000        0.000
Determination of surface currents             0.000        0.000
Calcul. of impedances/powers/losses           0.092        0.092
Calcul. of averaged SAR values                0.000        0.000
Calcul. of power ideal receiving ant.         0.000        0.000
Calcul. of cable coupling                     0.000        0.000
Calcul. of electric near field                0.000        0.000
Calcul. of magnetic near field                0.000        0.000
Calcul. of far field                          0.466        0.468
                            other              0.644        0.641
                                         -----------  -----------
                         total times:      31845.719    31845.719
               (total times in hours:          8.846        8.846)
Specified CPU-times are referring to the master process only
Sum of the CPU-times of all processes:   254765.749 seconds (   70.768 hours)
On average per process:                   31845.719 seconds (    8.846 hours)
Peak memory usage during the whole solution:   12.974 MByte
(refers to the master process only)
Sum of the peak memory of all processes:      103.782 MByte
On average per process:                        12.973 MByte

详细的报告。
1、MOM的时间主要用于构建矩阵和求解方程组。
2、MLFMM的时间主要是求解方程组。同时发现：
Calcul. of far field                          7.636        7.638
计算远场比MOM慢。
3、PO计算的时间全耗费在计算PO电流了，正因为多次反射导致了确定PO电流需要先考虑一次、再考虑二次激励来得到。
结论：PO的多次反射有点鸡肋，不适合处理两个面都很大的情况。MLFMM的确挺强的。
小编要是再做个多进程的并行对比，测试一下不同算法的加速比就更好了！

在略入射时 尤其高频会发生一些问题，比如遮蔽问题等等 5，85恰好是这个角度，所以才会那样

PO 2次
total times in hours:          8.846hr
  Physical Optics approximation or the Fock-theory is used for
  triangles with the following labels:
        Label                 PO/Fock  NOSHADE  MAXREF
              Cuboid1.Face1     PO        0         10
              Cuboid1.Face2     PO        0         10
  Meaning of NOSHADE:
   0 = Full ray tracing is performed, each side of the triangle
       can be illuminated.
   1 = No ray tracing, it is assumed that the triangle is directly
       illuminated by the sources and by the whole MoM region.
       The side is determined automatically.
   2 = Ray tracing is performed, however, the triangle can only
       be illuminated on the side from which the normal vector
       is pointing away, not on the back.
                    SUMMARY OF REQUIRED TIMES IN SECONDS
                                            CPU-time      runtime
Reading and constructing the geometry         0.453        0.453
Checking the geometry                         0.219        0.219
Initialisation of the Greens function         0.000        0.000
Calcul. of coupling for PO/Fock           31843.845    31843.846
Calcul. of matrix elements                    0.000        0.000
Calcul. of right-hand side vector             0.000        0.000
Preconditioning system of linear eqns.        0.000        0.000
Solution of the system of linear eqns.        0.000        0.000
Determination of surface currents             0.000        0.000
Calcul. of impedances/powers/losses           0.092        0.092
Calcul. of averaged SAR values                0.000        0.000
Calcul. of power ideal receiving ant.         0.000        0.000
Calcul. of cable coupling                     0.000        0.000
Calcul. of electric near field                0.000        0.000
Calcul. of magnetic near field                0.000        0.000
Calcul. of far field                          0.466        0.468
                            other              0.644        0.641
                                         -----------  -----------
                         total times:      31845.719    31845.719
               (total times in hours:          8.846        8.846)
Specified CPU-times are referring to the master process only
Sum of the CPU-times of all processes:   254765.749 seconds (   70.768 hours)
On average per process:                   31845.719 seconds (    8.846 hours)
Peak memory usage during the whole solution:   12.974 MByte
(refers to the master process only)
Sum of the peak memory of all processes:      103.782 MByte
On average per process:                        12.973 MByte

谁有二面角的算例，能否上传一下，我按材料上设置，每次算出来和测试值都不靠谱

是啊。传个模型上来阿！.cfx文件就行

算的模型对大呀，频率多高呀

認同您的說法..

http://bbs.rfeda.cn/read-htm-tid-14096.html

顶一下。

PO多次反射是不是只能在editfeko中设置?

我在 CADFEKO 沒看到...所以我在 EDIT 裡做。

学习了 谢谢

学习了，最基础的PO只计镜面反射