It seems to me that general orthogonal coordinates are quite popular in numerical treatments of PDEs. Sometimes people even use conformal maps to generate the locally orthogonal grids. But the actual meshes generated usually cannot preserve exactly right angles. So why the orthogonality matters? And what if certain orthogonality is lost due to the mesh generation process, what are the consequences? Could some one provide a systematic review on this matter? Thanks.
2026-03-28 07:00:00.1774681200
Why orthgonality matters for numerical treatment of PDEs?
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The big advantage of orthogonal transformation matrices in numerical computations is that orthogonal matrices are the only matrices with condition number one. If you multiply a matrix with a non-orthogonal matrix, the condition number of the matrix product is always larger than that of the original matrix. I hope this can help you.