Mixed Finite Element Analysis for an Elliptic/Mixed Elliptic Interface Problem with Jump Coefficients

Lan, Rihui; Sun, Pengtao; Mu, Mo

doi:10.1016/j.procs.2017.05.001

Cited by 7 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lumped-mass property (17) in Lemma 3.1 allows us to condense the inner product in subdomain Ω 1 to the interface Γ:…”

Section: Figure 1 Computational Domains With Interfacementioning

confidence: 99%

“…For comparison, let us first review a couple of typical decoupled methods by classical decoupling approaches in the literature. Algorithm 1 describes the decoupled Dirichlet-Neumann (DN) scheme [17,21] based on decoupling the implicit scheme from Problem ES h by applying the Dirichlet (3) and Neumann interface conditions (4) at alternating time levels with the use of computed data from the previous step on the other side of the interface during time marching.…”

Section: Figure 1 Computational Domains With Interfacementioning

confidence: 99%

“…On the other hand, certain partitioned approaches, often called loosely coupled, explicit coupling, or decoupled schemes, have also been investigated in the literature [2,4,5,7,13,14,15,17,19,20], where the sub-model in each domain is solved locally so that existing legacy solvers may be applied by easy software integration. There are many other important physical and numerical considerations that appeal to partitioned approaches for treating different sub-models in their own physical regions independently, particularly because of the very different physical properties and time scales.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Decoupling PDE computation with intrinsic or inertial Robin interface condition

Zhang

Cai

2021

era

Self Cite

View full text Add to dashboard Cite

We study decoupled numerical methods for multi-domain, multiphysics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical multi-modeling model problem, we derive an approximate intrinsic or inertial type Robin condition for its semi-discrete model. This new interface condition is justified both mathematically and physically in contrast to the classical Robin interface condition conventionally introduced for decoupling multi-modeling problems. Based on the intrinsic or inertial Robin condition, an equivalent semi-discrete model is introduced, which provides a general framework for devising effective decoupled numerical methods. Numerical experiments also confirm the effectiveness of this new decoupling approach.

show abstract

“…The lumped-mass property (17) in Lemma 3.1 allows us to condense the inner product in subdomain Ω 1 to the interface Γ:…”

Section: Figure 1 Computational Domains With Interfacementioning

confidence: 99%

Section: Figure 1 Computational Domains With Interfacementioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Decoupling PDE computation with intrinsic or inertial Robin interface condition

Zhang

Cai

2021

era

Self Cite

View full text Add to dashboard Cite

show abstract

“…For comparison, let us first review a couple of typical decoupled methods by classical decoupling approaches in the literature. Algorithm 4.1 describes the decoupled Dirichlet-Neumann (DN) scheme [15,19] based on decoupling the implicit scheme from Problem ES h by applying the Dirichlet (2.3) and Neumann interface conditions (2.4) at alternating time levels with the use of computed data from the previous step on the other side of the interface during time marching. For n = 1, 2, 3...N : 1.…”

Section: Decoupling Pde Computation With Intrinsic or Inertial Robin ...mentioning

confidence: 99%

Decoupling PDE Computation with Intrinsic or Inertial Robin Interface Condition

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical multi-modeling model problem, we derive an approximate intrinsic or inertial type Robin condition for its semi-discrete model. This new interface condition is justified both mathematically and physically in contrast to the classical Robin interface condition conventionally introduced for decoupling multi-modeling problems. Based on the intrinsic or inertial Robin condition, an equivalent semi-discrete model is introduced, which provides a general framework for devising effective decoupled numerical methods. Numerical experiments also confirm the effectiveness of this new decoupling approach.

show abstract

“…On the top of the monolithic approach, we adopt the ALE finite element method to discretize the presented FSI problem. As a type of body-fitted mesh method, ALE techniques [22,[26][27][28][29][30][31] have become the most accurate and also the most popular approach for solving FSI problems and other general moving boundary/interface problems within the frame of mixed finite element approximation [32][33][34][35][36][37][38], where the mesh on the interface is accommodated to be shared by both the fluid and the structure, and thus to automatically satisfy the interface conditions across the interface. On the other hand, considering that the microscopic process of the presented hemodynamic FSI is in equilibrium with the unchanged local macroscopic process of AAA progression, we employ the heterogeneous multiscale method (HMM) [39] to handle the multiscale challenge by combining our fully discrete ALE-FEM with a specific variable time-stepping approach.…”

Section: Introductionmentioning

confidence: 99%