Paper Citation Record · LEDGER

Multicontinuum splitting schemes for multiscale wave problems

As of 8 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2506.01670.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.01670 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:47:00.324380Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

39 of 39 outbound references displayed

verified exact0
verified fuzzy36
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e52487da-f2ca-4296-8094-19d2554f94e3 · outbound

This paper cites Sh-wave propagation in heterogeneous media: Velocity-stress finite-difference method.

Multicontinuum splitting schemes for multiscale wave problems Sh-wave propagation in heterogeneous media: Velocity-stress finite-difference method

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.406985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cb8608c1-f32e-4655-bbc3-e73049dc2a85 · outbound

This paper cites P-sv wave propagation in heterogeneous media: Velocity-stress finite-difference method.

Multicontinuum splitting schemes for multiscale wave problems P-sv wave propagation in heterogeneous media: Velocity-stress finite-difference method

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.386294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation df269022-375e-43b3-8251-968adb9917e1 · outbound

This paper cites Abdulle and P.

Multicontinuum splitting schemes for multiscale wave problems Abdulle and P

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.364105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9d97543c-375c-4f54-b29c-5eff4efae8ac · outbound

This paper cites Asymptotic analysis for periodic structures.

Multicontinuum splitting schemes for multiscale wave problems Asymptotic analysis for periodic structures

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.341912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation aeefc43a-bc12-486e-bcdc-10630cb5a11c · outbound

This paper cites Analysis of upscaling absolute permeability.

Multicontinuum splitting schemes for multiscale wave problems Analysis of upscaling absolute permeability

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.319118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31d8ceab-b537-4c57-953f-48d22e444727 · outbound

This paper cites Numerical homogenization of the acoustic wave equations with a continuum of scales.

Multicontinuum splitting schemes for multiscale wave problems Numerical homogenization of the acoustic wave equations with a continuum of scales

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.294089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d648aa4f-88e9-430b-8448-ffc8d3ee6374 · outbound

This paper cites Homogenization and porous media , volume 6.

Multicontinuum splitting schemes for multiscale wave problems Homogenization and porous media , volume 6

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.277294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ae0ddac6-cf0c-420f-a731-8fe65b461392 · outbound

This paper cites A multiscale finite element method for elliptic problems in composite materials and porous media.

Multicontinuum splitting schemes for multiscale wave problems A multiscale finite element method for elliptic problems in composite materials and porous media

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:48:04.256517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ed6c53f6-7e4c-47b6-9411-6962df7613fe · outbound

This paper cites Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients.

Multicontinuum splitting schemes for multiscale wave problems Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:52.195242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f6677233-5374-4485-acb9-0cfa83a5f564 · outbound

This paper cites Multiscale finite element methods: theory and applications , volume 4.

Multicontinuum splitting schemes for multiscale wave problems Multiscale finite element methods: theory and applications , volume 4

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:52.082926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 351020c0-c1ae-495a-bc93-79d9078d3bf3 · outbound

This paper cites Analysis of global multiscale finite element meth- ods for wave equations with continuum spatial scales.Applied numerical mathematics, 60(8):862–876, 2010.

Multicontinuum splitting schemes for multiscale wave problems Analysis of global multiscale finite element meth- ods for wave equations with continuum spatial scales.Applied numerical mathematics, 60(8):862–876, 2010

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:52.005600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d4fed29d-c017-4e7e-9610-60c83aa7e2d1 · outbound

This paper cites Localization of elliptic multiscale problems.

Multicontinuum splitting schemes for multiscale wave problems Localization of elliptic multiscale problems

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.919116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a6b4df1b-7f66-4328-b35a-7db1c4b9a92d · outbound

This paper cites Localized orthogonal decomposition techniques for boundary value problems.

Multicontinuum splitting schemes for multiscale wave problems Localized orthogonal decomposition techniques for boundary value problems

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.859023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4d3b4064-d665-44f2-8306-6192812a83cd · outbound

This paper cites Localized orthogonal decomposition method for the wave equation with a continuum of scales.

Multicontinuum splitting schemes for multiscale wave problems Localized orthogonal decomposition method for the wave equation with a continuum of scales

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.798534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2ea00ccf-7d74-4c29-88cb-f0ea769f2cb0 · outbound

This paper cites Generalized multiscale finite element methods (gmsfem).

Multicontinuum splitting schemes for multiscale wave problems Generalized multiscale finite element methods (gmsfem)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.659212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6286570e-cb22-42ab-bd22-8da951f14638 · outbound

This paper cites Generalized multiscale finite element methods for wave propagation in heterogeneous media.

Multicontinuum splitting schemes for multiscale wave problems Generalized multiscale finite element methods for wave propagation in heterogeneous media

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.486962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4d606c6d-9e7e-4023-825e-478ecefcc341 · outbound

This paper cites Generalized multiscale finite-element method (gmsfem) for elastic wave propagation in heterogeneous, anisotropic media.

Multicontinuum splitting schemes for multiscale wave problems Generalized multiscale finite-element method (gmsfem) for elastic wave propagation in heterogeneous, anisotropic media

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.260684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 217fbe07-7801-4a42-bd7d-ab884d21c106 · outbound

This paper cites Chung, Yalchin Efendiev, and Wing Tat Leung.

Multicontinuum splitting schemes for multiscale wave problems Chung, Yalchin Efendiev, and Wing Tat Leung

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:51.088008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bd9d6160-8a7e-43cb-a0a8-f6d332b406c1 · outbound

This paper cites Explicit and energy- conserving constraint energy minimizing generalized multiscale discontinuous galerkin method for wave propagation in heterogeneous media.

Multicontinuum splitting schemes for multiscale wave problems Explicit and energy- conserving constraint energy minimizing generalized multiscale discontinuous galerkin method for wave propagation in heterogeneous media

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.938262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cbc535fa-a6b2-4107-9347-290239ee6853 · outbound

This paper cites Multiscale Model Reduction: Multiscale Finite Element Methods and Their Generalizations , volume 212.

Multicontinuum splitting schemes for multiscale wave problems Multiscale Model Reduction: Multiscale Finite Element Methods and Their Generalizations , volume 212

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.864785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d0aaa8f7-f288-4956-b6c1-8c43f6327109 · outbound

This paper cites Heterogeneous multiscale methods: a review.

Multicontinuum splitting schemes for multiscale wave problems Heterogeneous multiscale methods: a review

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.760447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation be03bcd6-81bc-4aac-826f-539de9b0a280 · outbound

This paper cites The heterogeneous multiscale method.

Multicontinuum splitting schemes for multiscale wave problems The heterogeneous multiscale method

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.667013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b7c7ce1b-7c48-4a0b-a205-170dfbb27b73 · outbound

This paper cites Finite element heterogeneous multiscale method for the wave equation.

Multicontinuum splitting schemes for multiscale wave problems Finite element heterogeneous multiscale method for the wave equation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.586159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3c561fe6-d2ff-410a-96ad-173074b5907e · outbound

This paper cites The variational mul- tiscale method—a paradigm for computational mechanics.

Multicontinuum splitting schemes for multiscale wave problems The variational mul- tiscale method—a paradigm for computational mechanics

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.496648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c4aef0c5-1bcf-463d-a7b0-a5ffce36ef0b · outbound

This paper cites Chung, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, and Yating Wang.

Multicontinuum splitting schemes for multiscale wave problems Chung, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, and Yating Wang

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.407447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f1d9a689-b50a-4a09-bae2-2948a6a48819 · outbound

This paper cites Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media.

Multicontinuum splitting schemes for multiscale wave problems Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.309792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation beaffaa3-b234-43d0-ae48-e85f51f13faf · outbound

This paper cites Deep multiscale model learning.

Multicontinuum splitting schemes for multiscale wave problems Deep multiscale model learning

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.206089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6ebde747-71e5-40f5-995d-bbeddd150243 · outbound

This paper cites Hybrid explicit–implicit learning for multiscale problems with time dependent source.

Multicontinuum splitting schemes for multiscale wave problems Hybrid explicit–implicit learning for multiscale problems with time dependent source

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:50.077515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 96da346a-260d-477f-9244-d3c131c00605 · outbound

This paper cites Locally subspace-informed neural operators for efficient mul- tiscale pde solving.

Multicontinuum splitting schemes for multiscale wave problems Locally subspace-informed neural operators for efficient mul- tiscale pde solving

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T11:46:59.944324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d250975-059b-473e-b2c7-1f349347524e · outbound

This paper cites Multicontinuum homogenization and its relation to nonlocal multicontinuum theories.

Multicontinuum splitting schemes for multiscale wave problems Multicontinuum homogenization and its relation to nonlocal multicontinuum theories

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:49.986087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7017a0d9-61ce-4a83-ab0f-97e60b0bc01c · outbound

This paper cites Chung, Y.

Multicontinuum splitting schemes for multiscale wave problems Chung, Y

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:49.832551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 32765ed1-681c-4079-8d55-6b9c8ccb7a67 · outbound

This paper cites Multicontinuum homogeniza- tion for coupled flow and transport equations.

Multicontinuum splitting schemes for multiscale wave problems Multicontinuum homogeniza- tion for coupled flow and transport equations

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:49.715889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cee50f14-8d91-4095-8df1-e66c24f791cf · outbound

This paper cites Multicontinuum homogenization in perforated domains.

Multicontinuum splitting schemes for multiscale wave problems Multicontinuum homogenization in perforated domains

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:49.593549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e146c99f-1221-4367-a777-7944b33a8dea · outbound

This paper cites Contrast-independent partially explicit time discretizations for multiscale flow problems.Journal of Computational Physics, 445:110578, 2021.

Multicontinuum splitting schemes for multiscale wave problems Contrast-independent partially explicit time discretizations for multiscale flow problems.Journal of Computational Physics, 445:110578, 2021

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:00.788572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e18d93e0-c06f-4606-a8c4-49ed4c3072a8 · outbound

This paper cites Contrast-independent partially explicit time discretizations for multiscale wave problems.

Multicontinuum splitting schemes for multiscale wave problems Contrast-independent partially explicit time discretizations for multiscale wave problems

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:00.702103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9d9432c-9da4-44a4-b33a-5192b6baf239 · outbound

This paper cites Contrast-independent, partially- explicit time discretizations for nonlinear multiscale problems.

Multicontinuum splitting schemes for multiscale wave problems Contrast-independent, partially- explicit time discretizations for nonlinear multiscale problems

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:00.633578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 158d7c40-ea0a-4986-95f0-0a337425032a · outbound

This paper cites Multicontinuum splitting scheme for multiscale flow problems.

Multicontinuum splitting schemes for multiscale wave problems Multicontinuum splitting scheme for multiscale flow problems

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T11:47:00.244679Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 331e95c2-7edf-4abd-b280-d94f69e340d8 · outbound

This paper cites Some convergence analysis for multicontinuum homogenization.

Multicontinuum splitting schemes for multiscale wave problems Some convergence analysis for multicontinuum homogenization

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T11:47:00.280187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c99e8a08-79c1-4cf1-86b0-359936506d23 · outbound

This paper cites Strengthened cauchy-schwarz and h¨ older inequalities.

Multicontinuum splitting schemes for multiscale wave problems Strengthened cauchy-schwarz and h¨ older inequalities

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:47:00.566613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.