Assemble inverse operators using LU

[lvchien]

I found that inversion each diagonal block of the Gram matrix in multi-trace formulations is much faster than inversion the entire matrix.

[krcools]

This code does not relate to block diagonal operators does it?

I am also a bit sceptical of codifying the linear solver before assemble. This is in my view a breach of separation of responsibility.

I agree that control and perhaps automatic selection of linear solvers should be more extensive. Maybe we can rely on the existing work done in LinearSolve.jl. Or we can define a block diagonal invertor that either assumes the supplied LinearMap has the correct strcuture, or detects the block diagonal structure and throws an error if it is not compliant.

[krcools]

I have pushed the solution using generic LinearMaps onto master and added a representative use case in test/test_assemble_linearmap.

Does this solve your problem?

If so please close this PR

[lvchien]

Gram matrix in MTFs exhibits a super block-diagonal structure, where each diagonal block is again a 2x2 block-diagonal matrix. Your solution has resolved a local problem, where the inverse of Gram matrix can be copied over within the 2x2 matrix.

However, in the global scope, we still need to assemble the local Gram matrix for each subdomain beforehand (from my point of view), which is opposed to your principles in assembling the MTFs.

If your solution can resolve this global problem as well, please let me know. Otherwise, we are also thinking of a solution for that.

[krcools]

Can you add a test item and or example to your pr demonstrating what you have in mind?

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On Sat, 13 Dec 2025, 10:56 Le Van Chien, ***@***.***> wrote: *lvchien* left a comment (krcools/BEAST.jl#179) <#179 (comment)> Gram matrix in MTFs exhibits a super block-diagonal structure, where each diagonal block is again a 2x2 block-diagonal matrix. Your solution has resolved a local problem, where the inverse of Gram matrix can be copied over within the 2x2 matrix. However, in the global scope, we still need to assemble the local Gram matrix for each subdomain beforehand (from my point of view), which is opposed to your principles in assembling the MTFs. If your solution can resolve this global problem as well, please let me know. Otherwise, we are also thinking of a solution for that. — Reply to this email directly, view it on GitHub <#179 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACM6OAYQVQMC7DILDRURFPD4BPWGTAVCNFSM6AAAAACN45ZORSVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTMNBZGIYTEOBWGQ> . You are receiving this because you commented.Message ID: <krcools/BEAST. ***@***.***>