1818
1919# ╔═╡ 1a714fba-2a8e-11ec-182f-8f85cc17b02a
2020begin
21- using MeshArrays, CairoMakie, PlutoUI
21+ using MeshArrays, CairoMakie, PlutoUI, JLD2
2222 toc= PlutoUI. TableOfContents ()
2323
2424 md """
317317 D[findall (D .< 1. )] .= NaN
318318
319319 # Exchange funtions
320- Dexch= exchange (D,4 )
320+ # Dexch=MeshArrays.exchange_main(D,4)
321+ Dexch= exchange (D)
322+
321323 (dDdx, dDdy)= gradient (D,Γ)
322- (dDdxEx,dDdyEx)= exchange (dDdx,dDdy,4 )
324+ (dDdxEx,dDdyEx)= MeshArrays . exchange_main (dDdx,dDdy,4 )
323325
324326 # display
325327 PlutoUI. with_terminal () do
@@ -337,6 +339,12 @@ JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
337339MeshArrays = "cb8c808f-1acf-59a3-9d2b-6e38d009f683"
338340Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
339341PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
342+
343+ [compat]
344+ CairoMakie = "~0.15.8"
345+ JLD2 = "~0.6.3"
346+ MeshArrays = "~0.5.4"
347+ PlutoUI = "~0.7.79"
340348"""
341349
342350# ╔═╡ 00000000-0000-0000-0000-000000000002
@@ -345,7 +353,7 @@ PLUTO_MANIFEST_TOML_CONTENTS = """
345353
346354julia_version = "1.12.1"
347355manifest_format = "2.0"
348- project_hash = "014c3ca0ba2e6a0412eeed219248b04ab2494cdb "
356+ project_hash = "522926595610f15f3388401ce8173de31b9e2bd9 "
349357
350358[[deps.AbstractFFTs]]
351359deps = ["LinearAlgebra"]
@@ -661,9 +669,9 @@ uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
661669version = "2.2.4+0"
662670
663671[[deps.EnumX]]
664- git-tree-sha1 = "bddad79635af6aec424f53ed8aad5d7555dc6f00 "
672+ git-tree-sha1 = "7bebc8aad6ee6217c78c5ddcf7ed289d65d0263e "
665673uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
666- version = "1.0.5 "
674+ version = "1.0.6 "
667675
668676[[deps.ExactPredicates]]
669677deps = ["IntervalArithmetic", "Random", "StaticArrays"]
@@ -688,23 +696,17 @@ git-tree-sha1 = "01ba9d15e9eae375dc1eb9589df76b3572acd3f2"
688696uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
689697version = "8.0.1+0"
690698
691- [[deps.FFTW]]
692- deps = ["AbstractFFTs", "FFTW_jll", "Libdl", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
693- git-tree-sha1 = "97f08406df914023af55ade2f843c39e99c5d969"
694- uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
695- version = "1.10.0"
696-
697- [[deps.FFTW_jll]]
698- deps = ["Artifacts", "JLLWrappers", "Libdl"]
699- git-tree-sha1 = "6d6219a004b8cf1e0b4dbe27a2860b8e04eba0be"
700- uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
701- version = "3.3.11+0"
699+ [[deps.FFTA]]
700+ deps = ["AbstractFFTs", "DocStringExtensions", "LinearAlgebra", "MuladdMacro", "Primes", "Random", "Reexport"]
701+ git-tree-sha1 = "65e55303b72f4a567a51b174dd2c47496efeb95a"
702+ uuid = "b86e33f2-c0db-4aa1-a6e0-ab43e668529e"
703+ version = "0.3.1"
702704
703705[[deps.FileIO]]
704706deps = ["Pkg", "Requires", "UUIDs"]
705- git-tree-sha1 = "d60eb76f37d7e5a40cc2e7c36974d864b82dc802 "
707+ git-tree-sha1 = "6522cfb3b8fe97bec632252263057996cbd3de20 "
706708uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
707- version = "1.17.1 "
709+ version = "1.18.0 "
708710
709711 [deps.FileIO.extensions]
710712 HTTPExt = "HTTP"
@@ -841,9 +843,9 @@ version = "5.2.3+0"
841843
842844[[deps.Glib_jll]]
843845deps = ["Artifacts", "GettextRuntime_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
844- git-tree-sha1 = "6b4d2dc81736fe3980ff0e8879a9fc7c33c44ddf "
846+ git-tree-sha1 = "24f6def62397474a297bfcec22384101609142ed "
845847uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
846- version = "2.86.2 +0"
848+ version = "2.86.3 +0"
847849
848850[[deps.Glob]]
849851git-tree-sha1 = "83cb0092e2792b9e3a865b6655e88f5b862607e2"
@@ -898,9 +900,9 @@ version = "0.0.5"
898900
899901[[deps.HypertextLiteral]]
900902deps = ["Tricks"]
901- git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653 "
903+ git-tree-sha1 = "d1a86724f81bcd184a38fd284ce183ec067d71a0 "
902904uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
903- version = "0.9.5 "
905+ version = "1.0.0 "
904906
905907[[deps.IOCapture]]
906908deps = ["Logging", "Random"]
@@ -954,11 +956,10 @@ git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d"
954956uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
955957version = "0.1.5"
956958
957- [[deps.IntelOpenMP_jll]]
958- deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
959- git-tree-sha1 = "ec1debd61c300961f98064cfb21287613ad7f303"
960- uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
961- version = "2025.2.0+0"
959+ [[deps.IntegerMathUtils]]
960+ git-tree-sha1 = "4c1acff2dc6b6967e7e750633c50bc3b8d83e617"
961+ uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
962+ version = "0.1.3"
962963
963964[[deps.InteractiveUtils]]
964965deps = ["Markdown"]
@@ -1097,10 +1098,10 @@ uuid = "ac6e5ff7-fb65-4e79-a425-ec3bc9c03011"
10971098version = "1.12.0"
10981099
10991100[[deps.KernelDensity]]
1100- deps = ["Distributions", "DocStringExtensions", "FFTW ", "Interpolations", "StatsBase"]
1101- git-tree-sha1 = "ba51324b894edaf1df3ab16e2cc6bc3280a2f1a7 "
1101+ deps = ["Distributions", "DocStringExtensions", "FFTA ", "Interpolations", "StatsBase"]
1102+ git-tree-sha1 = "4260cfc991b8885bf747801fb60dd4503250e478 "
11021103uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
1103- version = "0.6.10 "
1104+ version = "0.6.11 "
11041105
11051106[[deps.LAME_jll]]
11061107deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -1190,9 +1191,9 @@ version = "1.18.0+0"
11901191
11911192[[deps.Libmount_jll]]
11921193deps = ["Artifacts", "JLLWrappers", "Libdl"]
1193- git-tree-sha1 = "3acf07f130a76f87c041cfb2ff7d7284ca67b072 "
1194+ git-tree-sha1 = "97bbca976196f2a1eb9607131cb108c69ec3f8a6 "
11941195uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
1195- version = "2.41.2 +0"
1196+ version = "2.41.3 +0"
11961197
11971198[[deps.Libtiff_jll]]
11981199deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
@@ -1202,9 +1203,9 @@ version = "4.7.2+0"
12021203
12031204[[deps.Libuuid_jll]]
12041205deps = ["Artifacts", "JLLWrappers", "Libdl"]
1205- git-tree-sha1 = "2a7a12fc0a4e7fb773450d17975322aa77142106 "
1206+ git-tree-sha1 = "d0205286d9eceadc518742860bf23f703779a3d6 "
12061207uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
1207- version = "2.41.2 +0"
1208+ version = "2.41.3 +0"
12081209
12091210[[deps.LinearAlgebra]]
12101211deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
@@ -1236,12 +1237,6 @@ git-tree-sha1 = "c64d943587f7187e751162b3b84445bbbd79f691"
12361237uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
12371238version = "1.1.0"
12381239
1239- [[deps.MKL_jll]]
1240- deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "oneTBB_jll"]
1241- git-tree-sha1 = "282cadc186e7b2ae0eeadbd7a4dffed4196ae2aa"
1242- uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
1243- version = "2025.2.0+0"
1244-
12451240[[deps.MacroTools]]
12461241git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522"
12471242uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
@@ -1277,9 +1272,9 @@ version = "0.6.7"
12771272
12781273[[deps.MeshArrays]]
12791274deps = ["CatViews", "Dates", "Distributed", "GeoInterface", "Glob", "LazyArtifacts", "NearestNeighbors", "Pkg", "Printf", "SharedArrays", "SparseArrays", "Statistics", "Unitful"]
1280- git-tree-sha1 = "19e7464371ad3af9f0c0f3a2aac718a772f6c578 "
1275+ git-tree-sha1 = "b9b1389807c4d535c046c8849fb05e752120c0bd "
12811276uuid = "cb8c808f-1acf-59a3-9d2b-6e38d009f683"
1282- version = "0.5.3 "
1277+ version = "0.5.4 "
12831278
12841279 [deps.MeshArrays.extensions]
12851280 MeshArraysDataDepsExt = ["DataDeps"]
@@ -1319,6 +1314,11 @@ version = "0.3.4"
13191314uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
13201315version = "2025.5.20"
13211316
1317+ [[deps.MuladdMacro]]
1318+ git-tree-sha1 = "cac9cc5499c25554cba55cd3c30543cff5ca4fab"
1319+ uuid = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
1320+ version = "0.2.4"
1321+
13221322[[deps.NaNMath]]
13231323deps = ["OpenLibm_jll"]
13241324git-tree-sha1 = "9b8215b1ee9e78a293f99797cd31375471b2bcae"
@@ -1327,9 +1327,9 @@ version = "1.1.3"
13271327
13281328[[deps.NearestNeighbors]]
13291329deps = ["AbstractTrees", "Distances", "StaticArrays"]
1330- git-tree-sha1 = "2949f294f82b5ad7192fd544a988a1e785438ee2 "
1330+ git-tree-sha1 = "e2c3bba08dd6dedfe17a17889131b885b8c082f0 "
13311331uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
1332- version = "0.4.26 "
1332+ version = "0.4.27 "
13331333
13341334[[deps.Netpbm]]
13351335deps = ["FileIO", "ImageCore", "ImageMetadata"]
@@ -1363,9 +1363,9 @@ version = "1.3.6+0"
13631363
13641364[[deps.OpenBLASConsistentFPCSR_jll]]
13651365deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
1366- git-tree-sha1 = "567515ca155d0020a45b05175449b499c63e7015 "
1366+ git-tree-sha1 = "f2b3b9e52a5eb6a3434c8cca67ad2dde011194f4 "
13671367uuid = "6cdc7f73-28fd-5e50-80fb-958a8875b1af"
1368- version = "0.3.29 +0"
1368+ version = "0.3.30 +0"
13691369
13701370[[deps.OpenBLAS_jll]]
13711371deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
@@ -1402,9 +1402,9 @@ version = "0.5.6+0"
14021402
14031403[[deps.Opus_jll]]
14041404deps = ["Artifacts", "JLLWrappers", "Libdl"]
1405- git-tree-sha1 = "39a11854f0cba27aa41efaedf43c77c5daa6be51 "
1405+ git-tree-sha1 = "e2bb57a313a74b8104064b7efd01406c0a50d2ff "
14061406uuid = "91d4177d-7536-5919-b921-800302f37372"
1407- version = "1.6.0 +0"
1407+ version = "1.6.1 +0"
14081408
14091409[[deps.OrderedCollections]]
14101410git-tree-sha1 = "05868e21324cede2207c6f0f466b4bfef6d5e7ee"
@@ -1485,9 +1485,9 @@ version = "1.4.4"
14851485
14861486[[deps.PlutoUI]]
14871487deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "Downloads", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
1488- git-tree-sha1 = "6122f9423393a2294e26a4efdf44960c5f8acb70 "
1488+ git-tree-sha1 = "3ac7038a98ef6977d44adeadc73cc6f596c08109 "
14891489uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
1490- version = "0.7.78 "
1490+ version = "0.7.79 "
14911491
14921492[[deps.PolygonOps]]
14931493git-tree-sha1 = "77b3d3605fc1cd0b42d95eba87dfcd2bf67d5ff6"
@@ -1506,6 +1506,12 @@ git-tree-sha1 = "522f093a29b31a93e34eaea17ba055d850edea28"
15061506uuid = "21216c6a-2e73-6563-6e65-726566657250"
15071507version = "1.5.1"
15081508
1509+ [[deps.Primes]]
1510+ deps = ["IntegerMathUtils"]
1511+ git-tree-sha1 = "25cdd1d20cd005b52fc12cb6be3f75faaf59bb9b"
1512+ uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
1513+ version = "0.5.7"
1514+
15091515[[deps.Printf]]
15101516deps = ["Unicode"]
15111517uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -1870,9 +1876,9 @@ version = "0.4.1"
18701876
18711877[[deps.Unitful]]
18721878deps = ["Dates", "LinearAlgebra", "Random"]
1873- git-tree-sha1 = "c25751629f5baaa27fef307f96536db62e1d754e "
1879+ git-tree-sha1 = "57e1b2c9de4bd6f40ecb9de4ac1797b81970d008 "
18741880uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
1875- version = "1.27 .0"
1881+ version = "1.28 .0"
18761882
18771883 [deps.Unitful.extensions]
18781884 ConstructionBaseUnitfulExt = "ConstructionBase"
@@ -2020,12 +2026,6 @@ deps = ["Artifacts", "Libdl"]
20202026uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
20212027version = "1.64.0+1"
20222028
2023- [[deps.oneTBB_jll]]
2024- deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
2025- git-tree-sha1 = "1350188a69a6e46f799d3945beef36435ed7262f"
2026- uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
2027- version = "2022.0.0+1"
2028-
20292029[[deps.p7zip_jll]]
20302030deps = ["Artifacts", "Libdl"]
20312031uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
@@ -2066,7 +2066,7 @@ version = "4.1.0+0"
20662066# ╠═6dfd7770-0197-4e74-ab27-bb666709c5d6
20672067# ╠═1bb1b658-7462-4837-8214-24618b9b343b
20682068# ╟─2c29ba59-ffc9-4763-8405-250029016ca5
2069- # ╠═ 169f9cdd-28f1-4574-ade4-237eab46a541
2069+ # ╟─ 169f9cdd-28f1-4574-ade4-237eab46a541
20702070# ╟─1a714fba-2a8e-11ec-182f-8f85cc17b02a
20712071# ╟─dec3cc17-bd5d-4fb0-a85c-df71a679264b
20722072# ╟─58f95665-9687-4b4f-af99-1239818f71a3
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