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Abstract Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed‐dimensional scalar elliptic problems. We design an effective preconditioner based on approximate block factorization and algebraic multigrid techniques. Numerical results on benchmarks with complex fracture structures demonstrate the effectiveness of the proposed linear solver and its robustness with respect to different physical and discretization parameters.
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Split Gröbner Bases for Satisfiability Modulo Finite Fields
Abstract Satisfiability modulo finite fields enables automated verification for cryptosystems. Unfortunately, previous solvers scale poorly for even some simple systems of field equations, in part because they build a full Gröbner basis (GB) for the system. We propose a new solver that uses multiple, simpler GBs instead of one full GB. Our solver, implemented within the cvc5 SMT solver, admits specialized propagation algorithms, e.g., for understanding bitsums. Experiments show that it solves important bitsum-heavy determinism benchmarks far faster than prior solvers, without introducing much overhead for other benchmarks.
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- Award ID(s):
- 2110397
- PAR ID:
- 10584605
- Editor(s):
- Gurfinkel, Arie; Ganesh, Vijay
- Publisher / Repository:
- Springer Nature Switzerland
- Date Published:
- Page Range / eLocation ID:
- 3 to 25
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Book Chapter:
- https://doi.org/10.1007/978-3-031-65627-9_1
