Commit 6ae131b6 authored by Theresa Pollinger's avatar Theresa Pollinger
Browse files

an interview notebook!

parent 5626bfe8
%% Cell type:code id: tags:
``` text
anything
```
%% Output
Hello, user! I am TheInterview, your partial differential equations and simulations expert. Let's set up a simulation together.
How many dimensions does your model have?
I am just assuming it's 1, since that is all we can currently handle.
What is the domain you would like to simulate for? Ω : type ❘ = [?;?], e.g. Ω = [0.0;1.0]
By the way, you can always try and use LaTeX-type input.
%% Cell type:code id: tags:
``` text
Ω = [0.0;1.0]
```
%% Output
we will just assume that the variable is called x for now.
Which variable(s) are you looking for? / What are the unknowns in your model? u : Ω → ??, e.g., u : Ω → ℝ ?
%% Cell type:code id: tags:
``` text
u : Ω → ℝ
```
%% Output
Ok, u : Ω → ℝ
u : Ω → ℝ
Would you like to name additional parameters like constants or functions (that are independent of your unknowns)? c : ℝ = ? or f : Ω → ℝ = ?
%% Cell type:code id: tags:
``` text
f = x
```
%% Output
Ok, f = [ x : Ω] x
Would you like to declare more parameters? [y/n]?
%% Cell type:code id: tags:
``` text
y
```
%% Output
%% Cell type:code id: tags:
``` text
\alpha = -5.0
```
%% Output
Ok, α = [ x : Ω] -5.0
Would you like to declare more parameters? [y/n]?
%% Cell type:code id: tags:
``` text
y
```
%% Output
%% Cell type:code id: tags:
``` text
k = x \cdot x
```
%% Output
I did not catch that. Could you please rephrase?
Details: MMT server error: unbound token: ·
%% Cell type:code id: tags:
``` text
n
```
%% Output
f = x
α = -5.0
Let's talk about your partial differential equation(s). What do they look like? Δu = 0.0, or laplace_operator Ω ℝ u = f ?
%% Cell type:code id: tags:
``` text
Δu = \alpha
```
%% Output
Ok, <result>
<xml>
<theory meta="http://mathhub.info/MitM/Foundation?Logic" base="http://mathhub.info/MitM/smglom/calculus" name="ephpde1">
<import from="http://mathhub.info/MitM/smglom/calculus?mDifferentialOperators"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?u"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?f"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?&#945;"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><constant name="mylhs">
<metadata><link resource="http://mathhub.info/MitM/smglom/calculus#1.0.1:35.0.35" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
<om:OMS name="Pi" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMBVAR><om:OMV name="anyu"><type><om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#19.0.19:23.0.23" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
</om:OMA></type></om:OMV></om:OMBVAR>
<om:OMA>
<om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
</om:OMA>
</om:OMBIND></om:OMOBJ></type>
<definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#10.0.10:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<om:OMS name="lambda" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMBVAR><om:OMV name="anyu"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#12.0.12:15.0.15" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata><type><om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#19.0.19:23.0.23" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
</om:OMA></type></om:OMV></om:OMBVAR>
<om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#27.0.27:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<om:OMS name="apply" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMS name="laplace_operator" module="mDifferentialOperators" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/><om:OMV name="anyu"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#29.0.29:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></om:OMV>
</om:OMA>
</om:OMBIND></om:OMOBJ></definition>
</constant><constant name="myrhs">
<metadata><link resource="http://mathhub.info/MitM/smglom/calculus#1.0.1:12.0.12" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
<om:OMS name="Pi" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
<om:OMBVAR><om:OMV name="x"><type><om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/></type></om:OMV></om:OMBVAR>
<om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
</om:OMBIND></om:OMOBJ></type>
<definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS name="&#945;" module="&#945;" base="http://mathhub.info/MitM/smglom/calculus"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#10.0.10:10.0.10" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></om:OMS></om:OMOBJ></definition>
</constant>
</theory>
</xml>
</result>
These are all the PDEs needed.
Let's discuss your boundary conditions. What do they look like? u(x) = f(x) or u(1.0) = \alpha ?
%% Cell type:code id: tags:
``` text
u = f
```
%% Output
Ok
These are all the boundary conditions needed.
Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils? [y/n]?
%% Cell type:code id: tags:
``` text
y
```
%% Output
Generated ExaStencils input.
%% Cell type:code id: tags:
``` text
```
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