Alexander,

I run step-8 and the system matrix is symmetry at least for the first 
cycle. I attach the output txt of the system matrix in this reply. Thanks.

Best,
Shanglong

在 2016年7月27日星期三 UTC-4上午10:53:46,Alexander写道:
>
> Shanglong,
> I'm not an expert in this field, but I assume it should be.
>
> Can you please check if system matrix in step-8 (which was used to 
> implement step-17) is symmetric?
>
> Alexander
>
> Am Mittwoch, 27. Juli 2016 15:58:42 UTC+2 schrieb shanglong zhang:
>>
>> Hi Alexander,
>>
>> Thank you for your explanation. I should have checked the symmetricity 
>> first.
>> However, since the step-17 is isotropic linear elasticity problem, should 
>> the system matrix be symmetry?
>>
>> Thank you very much for your help and patience.
>>
>> Regards,
>> Shanglong
>>
>> 在 2016年7月27日星期三 UTC-4上午4:49:53,Alexander写道:
>>>
>>> Shanglong,
>>> I can reproduce this behaviour, but this isn't a bug. I output the 
>>> 162x162 system matrix at first cycle and as far as I can see it fails 
>>> symmetry check. You can see this already from first few non-zero entries:
>>>
>>> (0,0) 1.33333
>>> (1,1) 1.33333
>>> (2,2) 1.33333
>>> (3,3) 1.33333
>>> (4,4) 1.33333
>>> (5,5) 1.33333
>>> (6,0) -0.666667
>>>
>>> See, there is no (0, 6) and symmetry is violated.
>>>
>>> The matrix is still positive-definite, that is probably why CG still 
>>> gets something out of it. 
>>>
>>> Alexander
>>>
>>>

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(0,0) 1.33333
(0,1) 0
(0,2) 0
(0,3) 0
(0,4) 0
(0,5) 0
(0,6) 0
(0,7) 0
(1,1) 1.33333
(1,0) 0
(1,2) 0
(1,3) 0
(1,4) 0
(1,5) 0
(1,6) 0
(1,7) 0
(2,2) 2.66667
(2,0) 0
(2,1) 0
(2,3) 0
(2,4) 0
(2,5) 0
(2,6) 0
(2,7) 0
(2,8) 0
(2,9) 0
(2,10) 0
(2,11) 0
(3,3) 2.66667
(3,0) 0
(3,1) 0
(3,2) 0
(3,4) 0
(3,5) 0
(3,6) 0
(3,7) 0
(3,8) 0
(3,9) 0
(3,10) 0
(3,11) 0
(4,4) 2.66667
(4,0) 0
(4,1) 0
(4,2) 0
(4,3) 0
(4,5) 0
(4,6) 0
(4,7) 0
(4,12) 0
(4,13) 0
(4,14) 0
(4,15) 0
(5,5) 2.66667
(5,0) 0
(5,1) 0
(5,2) 0
(5,3) 0
(5,4) 0
(5,6) 0
(5,7) 0
(5,12) 0
(5,13) 0
(5,14) 0
(5,15) 0
(6,6) 5.33333
(6,0) 0
(6,1) 0
(6,2) 0
(6,3) 0
(6,4) 0
(6,5) 0
(6,7) 0
(6,8) 0
(6,9) 0
(6,10) -1.66667
(6,11) 0
(6,12) 0
(6,13) 0
(6,14) 0.333333
(6,15) 0
(6,16) -0.666667
(6,17) -0.5
(7,7) 5.33333
(7,0) 0
(7,1) 0
(7,2) 0
(7,3) 0
(7,4) 0
(7,5) 0
(7,6) 0
(7,8) 0
(7,9) 0
(7,10) 0
(7,11) 0.333333
(7,12) 0
(7,13) 0
(7,14) 0
(7,15) -1.66667
(7,16) -0.5
(7,17) -0.666667
(8,8) 2.66667
(8,2) 0
(8,3) 0
(8,6) 0
(8,7) 0
(8,9) 0
(8,10) 0
(8,11) 0
(8,18) 0
(8,19) 0
(8,20) 0
(8,21) 0
(9,9) 2.66667
(9,2) 0
(9,3) 0
(9,6) 0
(9,7) 0
(9,8) 0
(9,10) 0
(9,11) 0
(9,18) 0
(9,19) 0
(9,20) 0
(9,21) 0
(10,10) 5.33333
(10,2) 0
(10,3) 0
(10,6) -1.66667
(10,7) 0
(10,8) 0
(10,9) 0
(10,11) 0
(10,14) -0.666667
(10,15) 0.5
(10,16) 0.333333
(10,17) 0
(10,18) 0
(10,19) 0
(10,20) -1.66667
(10,21) 0
(10,26) -0.666667
(10,27) -0.5
(11,11) 5.33333
(11,2) 0
(11,3) 0
(11,6) 0
(11,7) 0.333333
(11,8) 0
(11,9) 0
(11,10) 0
(11,14) 0.5
(11,15) -0.666667
(11,16) 0
(11,17) -1.66667
(11,18) 0
(11,19) 0
(11,20) 0
(11,21) 0.333333
(11,26) -0.5
(11,27) -0.666667
(12,12) 2.66667
(12,4) 0
(12,5) 0
(12,6) 0
(12,7) 0
(12,13) 0
(12,14) 0
(12,15) 0
(12,30) 0
(12,31) 0
(12,32) 0
(12,33) 0
(13,13) 2.66667
(13,4) 0
(13,5) 0
(13,6) 0
(13,7) 0
(13,12) 0
(13,14) 0
(13,15) 0
(13,30) 0
(13,31) 0
(13,32) 0
(13,33) 0
(14,14) 5.33333
(14,4) 0
(14,5) 0
(14,6) 0.333333
(14,7) 0
(14,10) -0.666667
(14,11) 0.5
(14,12) 0
(14,13) 0
(14,15) 0
(14,16) -1.66667
(14,17) 0
(14,30) 0
(14,31) 0
(14,32) 0.333333
(14,33) 0
(14,34) -0.666667
(14,35) -0.5
(15,15) 5.33333
(15,4) 0
(15,5) 0
(15,6) 0
(15,7) -1.66667
(15,10) 0.5
(15,11) -0.666667
(15,12) 0
(15,13) 0
(15,14) 0
(15,16) 0
(15,17) 0.333333
(15,30) 0
(15,31) 0
(15,32) 0
(15,33) -1.66667
(15,34) -0.5
(15,35) -0.666667
(16,16) 5.33333
(16,6) -0.666667
(16,7) -0.5
(16,10) 0.333333
(16,11) 0
(16,14) -1.66667
(16,15) 0
(16,17) 0
(16,20) -0.666667
(16,21) 0.5
(16,26) -1.66667
(16,27) 0
(16,32) -0.666667
(16,33) 0.5
(16,34) 0.333333
(16,35) 0
(16,42) -0.666667
(16,43) -0.5
(17,17) 5.33333
(17,6) -0.5
(17,7) -0.666667
(17,10) 0
(17,11) -1.66667
(17,14) 0
(17,15) 0.333333
(17,16) 0
(17,20) 0.5
(17,21) -0.666667
(17,26) 0
(17,27) 0.333333
(17,32) 0.5
(17,33) -0.666667
(17,34) 0
(17,35) -1.66667
(17,42) -0.5
(17,43) -0.666667
(18,18) 2.66667
(18,8) 0
(18,9) 0
(18,10) 0
(18,11) 0
(18,19) 0
(18,20) 0
(18,21) 0
(18,22) 0
(18,23) 0
(18,24) 0
(18,25) 0
(19,19) 2.66667
(19,8) 0
(19,9) 0
(19,10) 0
(19,11) 0
(19,18) 0
(19,20) 0
(19,21) 0
(19,22) 0
(19,23) 0
(19,24) 0
(19,25) 0
(20,20) 5.33333
(20,8) 0
(20,9) 0
(20,10) -1.66667
(20,11) 0
(20,16) -0.666667
(20,17) 0.5
(20,18) 0
(20,19) 0
(20,21) 0
(20,22) 0
(20,23) 0
(20,24) 0
(20,25) 0
(20,26) 0.333333
(20,27) 0
(20,28) 0
(20,29) 0
(21,21) 5.33333
(21,8) 0
(21,9) 0
(21,10) 0
(21,11) 0.333333
(21,16) 0.5
(21,17) -0.666667
(21,18) 0
(21,19) 0
(21,20) 0
(21,22) 0
(21,23) 0
(21,24) 0
(21,25) 0
(21,26) 0
(21,27) -1.66667
(21,28) 0
(21,29) 0
(22,22) 1.33333
(22,18) 0
(22,19) 0
(22,20) 0
(22,21) 0
(22,23) 0
(22,24) 0
(22,25) 0
(23,23) 1.33333
(23,18) 0
(23,19) 0
(23,20) 0
(23,21) 0
(23,22) 0
(23,24) 0
(23,25) 0
(24,24) 2.66667
(24,18) 0
(24,19) 0
(24,20) 0
(24,21) 0
(24,22) 0
(24,23) 0
(24,25) 0
(24,26) 0
(24,27) 0
(24,28) 0
(24,29) 0
(25,25) 2.66667
(25,18) 0
(25,19) 0
(25,20) 0
(25,21) 0
(25,22) 0
(25,23) 0
(25,24) 0
(25,26) 0
(25,27) 0
(25,28) 0
(25,29) 0
(26,26) 5.33333
(26,10) -0.666667
(26,11) -0.5
(26,16) -1.66667
(26,17) 0
(26,20) 0.333333
(26,21) 0
(26,24) 0
(26,25) 0
(26,27) 0
(26,28) 0
(26,29) 0
(26,34) -0.666667
(26,35) 0.5
(26,42) 0.333333
(26,43) 0
(26,44) 0
(26,45) 0
(27,27) 5.33333
(27,10) -0.5
(27,11) -0.666667
(27,16) 0
(27,17) 0.333333
(27,20) 0
(27,21) -1.66667
(27,24) 0
(27,25) 0
(27,26) 0
(27,28) 0
(27,29) 0
(27,34) 0.5
(27,35) -0.666667
(27,42) 0
(27,43) -1.66667
(27,44) 0
(27,45) 0
(28,28) 2.66667
(28,20) 0
(28,21) 0
(28,24) 0
(28,25) 0
(28,26) 0
(28,27) 0
(28,29) 0
(28,42) 0
(28,43) 0
(28,44) 0
(28,45) 0
(29,29) 2.66667
(29,20) 0
(29,21) 0
(29,24) 0
(29,25) 0
(29,26) 0
(29,27) 0
(29,28) 0
(29,42) 0
(29,43) 0
(29,44) 0
(29,45) 0
(30,30) 2.66667
(30,12) 0
(30,13) 0
(30,14) 0
(30,15) 0
(30,31) 0
(30,32) 0
(30,33) 0
(30,36) 0
(30,37) 0
(30,38) 0
(30,39) 0
(31,31) 2.66667
(31,12) 0
(31,13) 0
(31,14) 0
(31,15) 0
(31,30) 0
(31,32) 0
(31,33) 0
(31,36) 0
(31,37) 0
(31,38) 0
(31,39) 0
(32,32) 5.33333
(32,12) 0
(32,13) 0
(32,14) 0.333333
(32,15) 0
(32,16) -0.666667
(32,17) 0.5
(32,30) 0
(32,31) 0
(32,33) 0
(32,34) -1.66667
(32,35) 0
(32,36) 0
(32,37) 0
(32,38) 0
(32,39) 0
(32,40) 0
(32,41) 0
(33,33) 5.33333
(33,12) 0
(33,13) 0
(33,14) 0
(33,15) -1.66667
(33,16) 0.5
(33,17) -0.666667
(33,30) 0
(33,31) 0
(33,32) 0
(33,34) 0
(33,35) 0.333333
(33,36) 0
(33,37) 0
(33,38) 0
(33,39) 0
(33,40) 0
(33,41) 0
(34,34) 5.33333
(34,14) -0.666667
(34,15) -0.5
(34,16) 0.333333
(34,17) 0
(34,26) -0.666667
(34,27) 0.5
(34,32) -1.66667
(34,33) 0
(34,35) 0
(34,38) 0
(34,39) 0
(34,40) 0
(34,41) 0
(34,42) -1.66667
(34,43) 0
(34,46) 0
(34,47) 0
(35,35) 5.33333
(35,14) -0.5
(35,15) -0.666667
(35,16) 0
(35,17) -1.66667
(35,26) 0.5
(35,27) -0.666667
(35,32) 0
(35,33) 0.333333
(35,34) 0
(35,38) 0
(35,39) 0
(35,40) 0
(35,41) 0
(35,42) 0
(35,43) 0.333333
(35,46) 0
(35,47) 0
(36,36) 1.33333
(36,30) 0
(36,31) 0
(36,32) 0
(36,33) 0
(36,37) 0
(36,38) 0
(36,39) 0
(37,37) 1.33333
(37,30) 0
(37,31) 0
(37,32) 0
(37,33) 0
(37,36) 0
(37,38) 0
(37,39) 0
(38,38) 2.66667
(38,30) 0
(38,31) 0
(38,32) 0
(38,33) 0
(38,34) 0
(38,35) 0
(38,36) 0
(38,37) 0
(38,39) 0
(38,40) 0
(38,41) 0
(39,39) 2.66667
(39,30) 0
(39,31) 0
(39,32) 0
(39,33) 0
(39,34) 0
(39,35) 0
(39,36) 0
(39,37) 0
(39,38) 0
(39,40) 0
(39,41) 0
(40,40) 2.66667
(40,32) 0
(40,33) 0
(40,34) 0
(40,35) 0
(40,38) 0
(40,39) 0
(40,41) 0
(40,42) 0
(40,43) 0
(40,46) 0
(40,47) 0
(41,41) 2.66667
(41,32) 0
(41,33) 0
(41,34) 0
(41,35) 0
(41,38) 0
(41,39) 0
(41,40) 0
(41,42) 0
(41,43) 0
(41,46) 0
(41,47) 0
(42,42) 5.33333
(42,16) -0.666667
(42,17) -0.5
(42,26) 0.333333
(42,27) 0
(42,28) 0
(42,29) 0
(42,34) -1.66667
(42,35) 0
(42,40) 0
(42,41) 0
(42,43) 0
(42,44) 0
(42,45) 0
(42,46) 0
(42,47) 0
(42,48) 0
(42,49) 0
(43,43) 5.33333
(43,16) -0.5
(43,17) -0.666667
(43,26) 0
(43,27) -1.66667
(43,28) 0
(43,29) 0
(43,34) 0
(43,35) 0.333333
(43,40) 0
(43,41) 0
(43,42) 0
(43,44) 0
(43,45) 0
(43,46) 0
(43,47) 0
(43,48) 0
(43,49) 0
(44,44) 2.66667
(44,26) 0
(44,27) 0
(44,28) 0
(44,29) 0
(44,42) 0
(44,43) 0
(44,45) 0
(44,46) 0
(44,47) 0
(44,48) 0
(44,49) 0
(45,45) 2.66667
(45,26) 0
(45,27) 0
(45,28) 0
(45,29) 0
(45,42) 0
(45,43) 0
(45,44) 0
(45,46) 0
(45,47) 0
(45,48) 0
(45,49) 0
(46,46) 2.66667
(46,34) 0
(46,35) 0
(46,40) 0
(46,41) 0
(46,42) 0
(46,43) 0
(46,44) 0
(46,45) 0
(46,47) 0
(46,48) 0
(46,49) 0
(47,47) 2.66667
(47,34) 0
(47,35) 0
(47,40) 0
(47,41) 0
(47,42) 0
(47,43) 0
(47,44) 0
(47,45) 0
(47,46) 0
(47,48) 0
(47,49) 0
(48,48) 1.33333
(48,42) 0
(48,43) 0
(48,44) 0
(48,45) 0
(48,46) 0
(48,47) 0
(48,49) 0
(49,49) 1.33333
(49,42) 0
(49,43) 0
(49,44) 0
(49,45) 0
(49,46) 0
(49,47) 0
(49,48) 0

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