A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning
We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions h...
| Authors | Suchuan Dong, Yuchuan Zhang |
|---|---|
| Primary category | math.NA |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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