Fande,
I think you should just use AIJ, all the algorithms MatMult, MatFactor,
MatSolve when the matrix is diagonal are order n work with a relatively small
constant, and the overhead of using AIJ instead of a custom format is probably
at most a factor of three and since work is order n and it is a small constant
any gain would be lost in the much bigger constants for the rest of the
computation.

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Barry
I know Rich doesn't have unlimited money and suspect spending it on almost
anything else (like improving the load balancing in libMesh) will pay off far
far more.
> On Feb 14, 2018, at 8:29 PM, Jed Brown <j...@jedbrown.org> wrote:
>
> Fande Kong <fdkong...@gmail.com> writes:
>
>> On Wed, Feb 14, 2018 at 4:35 PM, Smith, Barry F. <bsm...@mcs.anl.gov> wrote:
>>
>>>
>>> What are you doing with the matrix?
>>>
>>
>> We are doing an explicit method. PDEs are discretized using a finite
>> element method, so there is a mass matrix. The mass matrix will be lumped,
>> and it becomes diagonal. We want to compute the inverse of the lumped
>> matrix, and also do a few of matrix-vector multiplications using the
>> lumped matrix or its inverse.
>>
>> The specific implementation won't make this more efficient?
>
> You can use pretty much any representation and you won't notice the time
> because you still have to apply the RHS operator and that is vastly more
> expensive.