arXiv:2610.09083v1 Announce Type: new Abstract: In this paper, we present JAXIGA, an open-source library for isogeometric analysis based on JAX. The library separates the construction of the mesh from the computations which are traced for compilation and differentiation. This allows geometry evaluation, assembly and the supported solvers to be combined in a just-in-time compiled program, for which first-order reverse-mode derivatives can be computed. We consider three numerical methods obtained from a single pointwise energy density. The Galerkin and energy-minimization methods use the same discrete potential and have the same stationary points, while collocation enforces the corresponding strong form. The sensitivities of a converged solution are obtained by solving one adjoint problem, and their accuracy depends on the tolerances of both the primal and adjoint problems. We also describe hierarchical extraction for local refinement of the variational methods and the use of smooth spline spaces for fourth-order problems. The numerical results are compared with analytical solutions and independent FEniCSx and JAX-FEM computations. For the reported GPU benchmark with 36,448 unknowns, assembly is twenty-four times faster than on the host CPU. When the conjugate-gradient solver is also run on the GPU, the total solution time is reduced from 31.8 to 1.38 seconds, and the result agrees with the direct solution to $5\times10^{-11}$. These results show that the choice of solver and the reuse of compilation are important for obtaining an overall reduction in computational cost.