Tutorial Part C, 02-runge-kutta; definitions.cpp

[moni]

Hello,

at the moment I’m working with Hermes2d for a composition about timeintegration and runge-kutta-methods.

I’ve got a question on the sourcecodes, in particular on the file definitions.cpp:

“ […] double CustomWeakFormHeatRK::CustomFormResidualSurf::value(int n, double *wt, Func<double> *u_ext[], Func<double> *v, Geom<double> *e,

ExtData<double> *ext) const”

What is the *wt about? It isn’t the testfunction, is it? Is the testfunction *v? And is u_ext[] the approximation for the original function T?

Moreover, I don’t get why there’s no lambda in the surface parts (Jacobian and Residual).

Looking forward to hearing from you soon.

Best wishes

Ramona Sasse

[Lukas Korous]

Hello,

Explanation of the parameters of the method

VectorForm::value(),

that is in your case

CustomWeakFormHeatRK::CustomFormResidualSurf::value,

is available at

http://hpfem.org/hermes/hermes/doc/_build/html/src/typical_example.html

"wt" is the vector of quadrature formula weights (properly adjusted by the reference mapping). There is "n" of them, that is the first parameter.

For other parameters, please check out the link I sent you.

What lambda do you have in mind?

Regards,
Lukas

--
You received this message because you are subscribed to the Google Groups "hermes2d" group.
To view this discussion on the web visit https://groups.google.com/d/msg/hermes2d/-/FnBYSzroUp8J.
To post to this group, send email to herm...@googlegroups.com.
To unsubscribe from this group, send email to hermes2d+u...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/hermes2d?hl=en.

--
Lukas Korous

[Pavel Solin]

Hi Ramona,

On Wed, Sep 5, 2012 at 3:52 AM, moni <ramona...@gmx.de> wrote:

Hello,

at the moment I’m working with Hermes2d for a composition about timeintegration and runge-kutta-methods.

I’ve got a question on the sourcecodes, in particular on the file definitions.cpp:

“ […] double CustomWeakFormHeatRK::CustomFormResidualSurf::value(int n, double *wt, Func<double> *u_ext[], Func<double> *v, Geom<double> *e,

ExtData<double> *ext) const”

What is the *wt about?

These are the integration weights.

 

It isn’t the testfunction, is it? Is the testfunction *v? And is u_ext[] the approximation for the original function T?

u_ext are previous Newton solutions (just one if you have a single equation).

 

Moreover, I don’t get why there’s no lambda in the surface parts (Jacobian and Residual).

There is lambda on lines 3, 7, and 13 in definitions.cpp. It is also 

present in the header of the constructor in definitions.h.

HTH, feel free to ask more :)

Pavel

 

Looking forward to hearing from you soon.

Best wishes

Ramona Sasse

--
You received this message because you are subscribed to the Google Groups "hermes2d" group.
To view this discussion on the web visit https://groups.google.com/d/msg/hermes2d/-/FnBYSzroUp8J.
To post to this group, send email to herm...@googlegroups.com.
To unsubscribe from this group, send email to hermes2d+u...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/hermes2d?hl=en.

--

Pavel Solin

Associate Professor

Applied and Computational Mathematics

University of Nevada, Reno

http://hpfem.org/~pavel

[moni]

Hey,

thanks for your last quick answers. 

I'm still working on my composition and I'd like to compare numerically a few methods (Implicit_SDIRK_2_2, Implicit_Crank_Nicolson_2_2, Implicit_SDIRK_CASH_3_23,  Implicit_SDIRK_CASH_5_24)  using the tutorial part C-transient.

So far I tried to count the CPU-time with clock () and compared respectively the values. I also compare the graphics at specific timesteps (t=28800.00 s, t=57600.00 s, t=85500.00 s). But like "there's no proof with pictures" I'm looking for some error estimator. Is it possible to get an error estimator in this programme? I'm not sure if there's one for the first two methods above. But the embedded methods already have two approximations, haven't they? So can I use the two approx. maybe to make an aposteriori error estimation? How can I implement such one in the code? 

Looking forward to your reply.

Regards,

Ramona

[moni]

I've got another question...

Does the programm P03-02-runge-kutta use hpFEM or (bi-)linear FEM?