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Removing parallel citation to HPS method.
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DamynChipman committed Apr 20, 2024
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# Summary

EllipticForest is a software library with utilities to solve elliptic partial differential equations (PDEs) with adaptive mesh refinement (AMR) using a direct matrix factorization. It implements a quadtree-adaptive variation of the Hierarchical Poincaré-Steklov (HPS) method [@gillman2014direct]. The HPS method is a direct method for solving elliptic PDEs based on the recursive merging of Poincaré-Steklov operators [@quarteroni1991theory]. EllipticForest is built on top of the parallel and highly efficient mesh library `p4est` [@burstedde2011p4est] for mesh adaptivity and mesh management. Distributed memory parallelism is implemented through the Message Passing Interface (MPI) [@mpi41]. EllipticForest wraps the fast, cyclic-reduction methods found in the FISHPACK [@swarztrauber1999fishpack] library and updated in the FISHPACK90 [@adams2016fishpack90] library at the lowest grid level (called leaf patches). In addition, for more general elliptic problems, EllipticForest wraps solvers from the PDE solver library PETSc [@anl2023petsc]. The numerical methods used in EllipticForest are detailed in [@chipman2024fast] and the parallel counterpart in [@chipman2024parallel]. A key feature of EllipticForest is the ability for users to extend the solver interface classes to implement custom solvers on leaf patches. EllipticForest is an implementation of the HPS method to be used as a software library, either as a standalone to solve elliptic PDEs or for coupling with other scientific libraries for broader applications.
EllipticForest is a software library with utilities to solve elliptic partial differential equations (PDEs) with adaptive mesh refinement (AMR) using a direct matrix factorization. It implements a quadtree-adaptive variation of the Hierarchical Poincaré-Steklov (HPS) method [@gillman2014direct]. The HPS method is a direct method for solving elliptic PDEs based on the recursive merging of Poincaré-Steklov operators [@quarteroni1991theory]. EllipticForest is built on top of the parallel and highly efficient mesh library `p4est` [@burstedde2011p4est] for mesh adaptivity and mesh management. Distributed memory parallelism is implemented through the Message Passing Interface (MPI) [@mpi41]. EllipticForest wraps the fast, cyclic-reduction methods found in the FISHPACK [@swarztrauber1999fishpack] library and updated in the FISHPACK90 [@adams2016fishpack90] library at the lowest grid level (called leaf patches). In addition, for more general elliptic problems, EllipticForest wraps solvers from the PDE solver library PETSc [@anl2023petsc]. The numerical methods used in EllipticForest are detailed in [@chipman2024fast]. A key feature of EllipticForest is the ability for users to extend the solver interface classes to implement custom solvers on leaf patches. EllipticForest is an implementation of the HPS method to be used as a software library, either as a standalone to solve elliptic PDEs or for coupling with other scientific libraries for broader applications.

# Statement of Need

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