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Subtracting a 2D quantity from a 1D quantity
Posted 18.05.2017, 17:07 GMT-4 2 Replies
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I have a 2D model of the concentration of ions diffusing over time, c(t,x,y). I figured out how to calculate an average over 1 dimension, viz. y, i.e, the variable upper limit integral of c_avg(t,x,y) = 3/(y^3) ∫ c(t,x,z) z^2 dz from 0 to y (z is a dummy variable for y) by using the Coefficient Form PDE. The value of y ranges from 0 to 1.
I would like to use the value of the average where y = 1 (average concentration over the entire range of y) & subtract all values of the average from it, i.e., c_avg(t,x,1) - c_avg(t,x,y). Is there a simple way to do this?
I would like to use the value of the average where y = 1 (average concentration over the entire range of y) & subtract all values of the average from it, i.e., c_avg(t,x,1) - c_avg(t,x,y). Is there a simple way to do this?
2 Replies Last Post 19.05.2017, 11:27 GMT-4
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Posted:
8 years ago
Hi Clyde
I'm sure that I fully understand what you are trying to do, but it should be possible to calculate the integral using projection couplings. See this section "EXAMPLES OF PROJECTION COUPLINGS" in the Reference Manual for some examples.
--
Lars Gregersen
Comsol Denmark
I'm sure that I fully understand what you are trying to do, but it should be possible to calculate the integral using projection couplings. See this section "EXAMPLES OF PROJECTION COUPLINGS" in the Reference Manual for some examples.
--
Lars Gregersen
Comsol Denmark
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Posted:
8 years ago
Updated:
8 years ago
Thanks Lars,
I had reviewed the section on Extrusion, Projection, & Scalar coupling operators; however, the examples in the Reference Manual were a bit vague. Would you know of a good resource showing a practical example?
As for what I'm working with, I have values of ion concentration over a simulated 2D contour over time, using an Extremely Fine Rectangular Mesh. The contour results in a 41 x 41 value matrix at each instance in time. To simply my scenario, let me illustrate with a 3 x 3 matrix: Let c(x,y,t) at t = tn be
| 2.4 4.5 5.1 | = | c(0,2,tn) c(1,2,tn) c(2,2,tn) |
| 1.3 3.6 1.8 | = | c(0,1,tn) c(1,1,tn) c(2,1,tn) |
| 0.7 1.2 0.3 | = | c(0,0,tn) c(1,0,tn) c(2,0,tn) |
Using Coefficient Form PDE, I can calculate the average over y as:
| 1.5 3.1 2.4 | = | <c(x,2,tn)>: this row is the mean of c(x,0,tn), c(x,1,tn), c(x,2,tn)
| 1.0 2.4 1.1 | = | <c(x,1,tn)>: this row is the mean of c(x,0,tn), c(x,1,tn)
| 0.7 1.2 0.3 | = | <c(x,0,tn)>: this row is just c(x,0,tn)
Now, I'd like to take the values of <c(x,2,tn)> copied over all rows to subtract c(x,y,tn), i.e.,
| 1.5 3.1 2.4 | - | 2.4 4.5 5.1 |
| 1.5 3.1 2.4 | - | 1.3 3.6 1.8 |
| 1.5 3.1 2.4 | - | 0.7 1.2 0.3 |
I'm thinking a Linear Extrusion would be the method to use. Would this be the best approach?
I had reviewed the section on Extrusion, Projection, & Scalar coupling operators; however, the examples in the Reference Manual were a bit vague. Would you know of a good resource showing a practical example?
As for what I'm working with, I have values of ion concentration over a simulated 2D contour over time, using an Extremely Fine Rectangular Mesh. The contour results in a 41 x 41 value matrix at each instance in time. To simply my scenario, let me illustrate with a 3 x 3 matrix: Let c(x,y,t) at t = tn be
| 2.4 4.5 5.1 | = | c(0,2,tn) c(1,2,tn) c(2,2,tn) |
| 1.3 3.6 1.8 | = | c(0,1,tn) c(1,1,tn) c(2,1,tn) |
| 0.7 1.2 0.3 | = | c(0,0,tn) c(1,0,tn) c(2,0,tn) |
Using Coefficient Form PDE, I can calculate the average over y as:
| 1.5 3.1 2.4 | = | <c(x,2,tn)>: this row is the mean of c(x,0,tn), c(x,1,tn), c(x,2,tn)
| 1.0 2.4 1.1 | = | <c(x,1,tn)>: this row is the mean of c(x,0,tn), c(x,1,tn)
| 0.7 1.2 0.3 | = | <c(x,0,tn)>: this row is just c(x,0,tn)
Now, I'd like to take the values of <c(x,2,tn)> copied over all rows to subtract c(x,y,tn), i.e.,
| 1.5 3.1 2.4 | - | 2.4 4.5 5.1 |
| 1.5 3.1 2.4 | - | 1.3 3.6 1.8 |
| 1.5 3.1 2.4 | - | 0.7 1.2 0.3 |
I'm thinking a Linear Extrusion would be the method to use. Would this be the best approach?