Sparse Equation Solver with Unrolling Strategies

Nguyen, Duc T.

doi:10.1007/978-1-4615-1337-7_10

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…Since 1990s, direct solution techniques of finite element analysis [4] have developed from conventional variable bandwidth [5] or frontal solutions [6] to various sparse solutions [5,[7][8][9][10][11], such as backward-reference (left-looking), forwardreference (right-looking), and multifrontal [12,13] methods. They have yielded a breakthrough in terms of solution speed and storage requirement in finite element analysis.…”

Section: Sparse Direct Solution Techniquesmentioning

confidence: 99%

“…There are six different forms [17] to implement LDL T factorization, which are six permutations of the indices , , . Row-sparse factorization [21] and its improvement [8,18] are foundations of the present sparse solution implementation, in which form and its variations are used. The simple form can be expressed in terms of tasks [18,22]:…”

Section: Effect Of Local Change In Sparse Solutionmentioning

confidence: 99%

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Partial Refactorization in Sparse Matrix Solution: A New Possibility for Faster Nonlinear Finite Element Analysis

Song

Chen

Sun

2013

Mathematical Problems in Engineering

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This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.

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Section: Sparse Direct Solution Techniquesmentioning

confidence: 99%

Section: Effect Of Local Change In Sparse Solutionmentioning

confidence: 99%

Partial Refactorization in Sparse Matrix Solution: A New Possibility for Faster Nonlinear Finite Element Analysis

Song

Chen

Sun

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…In reference (Nguyen, 1997) the super-equation was introduced to sparse matrix computation with the conventional sparse storage scheme for the factor L T of K in order to perform one-way unrolling.…”

Section: Introductionmentioning

confidence: 99%