Manav Bhatia manav at u.washington.edu
Wed Feb 21 00:28:48 CST 2007

On Feb 20, 2007, at 9:16 PM, Hong Zhang wrote:

> On Tue, 20 Feb 2007, Manav Bhatia wrote:
>> So, if I have a problem with a LHS matrix, and I want to use an
>> explicit method, then do I have to invert the matrix before asking
>> the solver to run? i.e. the solver will not do that for me?
> The LHS matrix formulation is not implemented for the explicit method.
> Do you have such application?

Well, I am working with a conduction heat transfer finite element  
model, which has the following equation set:

[C(t,{T})] d{T}/dt = {F(t,{T})} - [K(t,{T})] {T}

with initial conditions
{T(0)} = {T0}

So, I have a problem which has a LHS matrix, which is also dependent  
on the primary variable (which is temperature {T}).
In the simple case, ofcourse, we can neglect this dependence on  
temperature (for [C]), but that has limited applicability for my  
problem, since the [C] matrix has non-negligible nonlinearities.
So, I am looking for ways to formulate my problem to use the Petsc  
solvers. The best option that I can think  of is to restate the  
problem as:

d{T}/dt = [C(t,{T})]^(-1) ({F(t,{T})} - [K(t,{T})] {T})

where I can now specify the RHS function and its jacobian (I will  
provide the jacobian, so no need to use finite differencing), and use  
an explicit / implicit solver.

However, if I assume a linear problem, then I am left with a case of

[C] d{T}/dt = {F(t)} - [K]{T}

Here, I could either restate the problem in the same way as I did  
above, or I could specify a LHS matrix (in this case [C]), and ask  
the solver to handle it. But, from our previous email exchanges, it  
seems like I will have to use an implicit solver for the same, since  
an explicit solver will not handle a LHS matrix.

Kindly correct me if I am wrong.


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